AMA4601 mini project
Leung Chun Kit(21018713D), Lam Wai Tsun(21019252D)
Time series analysis on air pollutants data from Wanshouxigong(Beijing) air-quality monitoring site
Data source: https://archive.ics.uci.edu/ml/datasets/Beijing+Multi-Site+Air-Quality+Data
The data set includes hourly air pollutants data from 12 nationally-controlled air-quality monitoring sites. The air-quality data are from the Beijing Municipal Environmental Monitoring Center. The meteorological data in each air-quality site are matched with the nearest weather station from the China Meteorological Administration. The time period is from March 1st, 2013 to February 28th, 2017. Missing data are denoted as NA.
Attribute Information:
No: row number
year: year of data in this row
month: month of data in this row
day: day of data in this row
hour: hour of data in this row
PM2.5: PM2.5 concentration (ug/m^3)
PM10: PM10 concentration (ug/m^3)
SO2: SO2 concentration (ug/m^3)
NO2: NO2 concentration (ug/m^3)
CO: CO concentration (ug/m^3)
O3: O3 concentration (ug/m^3)
TEMP: temperature (degree Celsius)
PRES: pressure (hPa)
DEWP: dew point temperature (degree Celsius)
RAIN: precipitation (mm)
wd: wind direction
WSPM: wind speed (m/s)
station: name of the air-quality monitoring site
loading library
library(corrplot)
library(RColorBrewer)
library(tidyr)
library(dplyr)
library(data.table)
library(seasonal)
library(forecast)
library(dplyr)
library(TSstudio)
library(xts)
library(tseries)
library(ggplot2)
library(lattice)data <- read.csv("PRSA_Data_Wanshouxigong_20130301-20170228.csv", header = TRUE)We are going to study the air pollution condition in Beijing, Wanshou xigong.
attach(data)Checking the number of missing value
sum(is.na(data))## [1] 5146There are 5146 cells contain missing values.
fill the missing value
column_nane_list <- colnames(data)
for (a in column_nane_list){
data <-data %>% fill(a,.direction = 'updown')
}## Warning: Using an external vector in selections was deprecated in tidyselect 1.1.0.
## ℹ Please use `all_of()` or `any_of()` instead.
## # Was:
## data %>% select(a)
##
## # Now:
## data %>% select(all_of(a))
##
## See <https://tidyselect.r-lib.org/reference/faq-external-vector.html>.sum( apply(data,2, function(x) is.na(x)))## [1] 0We fill the missing values by the previous value.If the previous value is not available, we will fill by the next value.
aggregate data, group the data by year, month and day
There are two type of information in the data set. One is the different index of the air pollutants (e.g. PM2.5, PM10, SO2, NO2, CO, O3). And the other type is the weather condition (e.g. TEMP, PRES, DEWP, RAIN, wd, WSPM).
grouped_year = aggregate(cbind(PM2.5,PM10,SO2,NO2,CO,O3,TEMP,PRES,DEWP,RAIN,WSPM) ~ data$year, data = data, FUN = mean, na.rm = TRUE)
grouped_month = aggregate(cbind(PM2.5,PM10,SO2,NO2,CO,O3,TEMP,PRES, DEWP,RAIN,WSPM) ~ data$year+ data$month, data = data, FUN = mean, na.rm = TRUE)
grouped_day = aggregate(cbind(PM2.5,PM10,SO2,NO2,CO,O3,TEMP,PRES, DEWP,RAIN,WSPM) ~ data$year+ data$month + data$day, data = data, FUN = mean, na.rm = TRUE)
grouped_year <- grouped_year[
order( grouped_year[,1] ),
]
grouped_month <- grouped_month[
order( grouped_month[,1], grouped_month[,2] ),
]
grouped_day <- grouped_day[
order( grouped_day[,1], grouped_day[,2], grouped_day[,3] ),
]we first analysis the monthly data
Plot the linear correlation between diffrent variable
corr_month <- cor(grouped_month[,-c(1:2)])
corrplot(corr_month, type="upper", order="hclust",
col=brewer.pal(n=8, name="RdYlBu"))
We have found that the air pollutants have high correlation between each other (e.g. PM2.5, PM10, CO, SO2 and NO2 has positive correlation, but O3 has the negativity correlation with other air pollutants.)
And we also have found that the weather conditions also have high correlation with the air pollutants (e.g temperature, precipitation has negativity correlation with air pollutant(PM2.5,PM10, CO, SO2, NO2))
convert dataframe to timeframe object
grouped_month <- grouped_month [,-c(1:2)]
ts_by_month <- ts(grouped_month , start = c(2013, 3), frequency = 12)variables against time plot
plot.ts(ts_by_month[,1:6])
plot.ts(ts_by_month[,7:11])
plot the box plot for variable in the cycle (month)
# cycle(ts_by_month)
boxplot(ts_by_month [,'PM2.5'] ~ cycle(ts_by_month [,'PM2.5']))
boxplot(ts_by_month [,'PM10'] ~ cycle(ts_by_month [,'PM10']))
boxplot(ts_by_month [,'SO2'] ~ cycle(ts_by_month [,'SO2']))
boxplot(ts_by_month [,'NO2'] ~ cycle(ts_by_month [,'NO2']))
boxplot(ts_by_month [,'CO'] ~ cycle(ts_by_month [,'CO']))
boxplot(ts_by_month [,'O3'] ~ cycle(ts_by_month [,'O3']))
boxplot(ts_by_month [,'TEMP'] ~ cycle(ts_by_month [,'TEMP']))
boxplot(ts_by_month [,'DEWP'] ~ cycle(ts_by_month [,'DEWP']))
boxplot(ts_by_month [,'PRES'] ~ cycle(ts_by_month [,'PRES']))
boxplot(ts_by_month [,'RAIN'] ~ cycle(ts_by_month [,'RAIN']))
boxplot(ts_by_month [,'WSPM'] ~ cycle(ts_by_month [,'WSPM']))
We can observe the distribution of difference variable among month
There are periodic pattern among month.
For example, the PM2.5 concentration is lower and less variate at May to Sept, but higher and more variate at Dec to Feb.
The precipitation is more variate at summer (Especially July).
Plot the heat map
ts_heatmap(ts_by_month[,'PM2.5'],title = " Heatmap - the PM2.5 concentration in Wanshou xigong")ts_heatmap(ts_by_month[,'PM10'],title = " Heatmap - the PM10 concentration in Wanshou xigong")ts_heatmap(ts_by_month[,'SO2'],title = " Heatmap - the SO2 concentration in Wanshou xigong")ts_heatmap(ts_by_month[,'NO2'],title = " Heatmap - the NO2 concentration in Wanshou xigong")ts_heatmap(ts_by_month[,'CO'],title = " Heatmap - the CO concentration in Wanshou xigong")ts_heatmap(ts_by_month[,'O3'],title = " Heatmap - the O3 concentration in Wanshou xigong")ts_heatmap(ts_by_month[,'TEMP'],title = " Heatmap - the TEMP in Wanshou xigong")ts_heatmap(ts_by_month[,'PRES'],title = " Heatmap - the PRES in Wanshou xigong")ts_heatmap(ts_by_month[,'RAIN'],title = " Heatmap - the RAIN in Wanshou xigong")The heat maps shows the level of the variable. The darker color means that the level is higher.
For example, the PM2.5 concentration level is higher in winter than summer. The Temperature is higher in summer than winter.
Weekly Analysis
convert_date_to_weekday <- function(day, month, year){
date <- as.POSIXlt(paste(as.character(year) , as.character(month), as.character(day), sep="-"), tz = "UTC")
weekday <- weekdays(date)
return (weekday)
}data_weekday <- data
data_weekday$weekday <- mapply(convert_date_to_weekday, data$day, data$month, data$year)
grouped_weekday_year = aggregate(cbind(PM2.5,PM10,SO2,NO2,CO,O3,TEMP,PRES, DEWP,RAIN,WSPM) ~ weekday , data = data_weekday, FUN = mean, na.rm = TRUE)
grouped_weekday_year$weekday <- factor(grouped_weekday_year$weekday, levels = c("Monday", "Tuesday","Wednesday","Thursday", "Friday","Saturday","Sunday"))
weekdayorder = c("Monday", "Tuesday","Wednesday","Thursday", "Friday","Saturday","Sunday")
grouped_weekday_year = grouped_weekday_year[order(match(grouped_weekday_year$weekday,weekdayorder)),]
xyplot( PM2.5 ~ weekday ,
type="b",
data = grouped_weekday_year,
auto.key = TRUE,
)
xyplot( PM10 ~ weekday ,
type="b",
data = grouped_weekday_year,
auto.key = TRUE,
)
xyplot( CO ~ weekday ,
type="b",
data = grouped_weekday_year,
auto.key = TRUE,
)
xyplot( NO2 ~ weekday ,
type="b",
data = grouped_weekday_year,
auto.key = TRUE,
)
xyplot( SO2 ~ weekday ,
type="b",
data = grouped_weekday_year,
auto.key = TRUE,
)
xyplot( O3 ~ weekday ,
type="b",
data = grouped_weekday_year,
auto.key = TRUE,
)
xyplot( TEMP ~ weekday ,
type="b",
data = grouped_weekday_year,
auto.key = TRUE,
ylim =c (10,15)
)
xyplot( RAIN ~ weekday ,
type="b",
data = grouped_weekday_year,
auto.key = TRUE,
ylim =c (0,0.2)
)
xyplot( PRES ~ weekday ,
type="b",
data = grouped_weekday_year,
auto.key = TRUE,
ylim =c (900,1100)
)
For the air pollutant, Here are some variations among weekdays. For example, Staturday has higher PM2.5, PM10, CO, NO2 concentration.
For the weather conditions, there are not much variation among weekdays. (It is normal because the weather should not by affect by the week time )
Hourly analysis
grouped_hour = aggregate(cbind(PM2.5,PM10,SO2,NO2,CO,O3,TEMP,PRES, DEWP,RAIN,WSPM) ~ hour , data = data, FUN = mean, na.rm = TRUE)
grouped_hour_month = aggregate(cbind(PM2.5,PM10,SO2,NO2,CO,O3,TEMP,PRES, DEWP,RAIN,WSPM) ~ hour + month , data = data, FUN = mean, na.rm = TRUE)
xyplot( PM2.5 ~ hour ,
type="b",
data = grouped_hour,
auto.key = TRUE,
)
xyplot( PM10 ~ hour ,
type="b",
data = grouped_hour,
auto.key = TRUE,
)
xyplot( CO ~ hour ,
type="b",
data = grouped_hour,
auto.key = TRUE,
)
xyplot( NO2 ~ hour ,
type="b",
data = grouped_hour,
auto.key = TRUE,
)
xyplot( SO2 ~ hour ,
type="b",
data = grouped_hour,
auto.key = TRUE,
)
xyplot( O3 ~ hour ,
type="b",
data = grouped_hour,
auto.key = TRUE,
)
xyplot( TEMP ~ hour ,
type="b",
data = grouped_hour,
auto.key = TRUE,
)
xyplot( RAIN ~ hour ,
type="b",
data = grouped_hour,
auto.key = TRUE,
ylim =c (0,0.2)
)
xyplot( PRES ~ hour ,
type="b",
data = grouped_hour,
auto.key = TRUE,
ylim =c (900,1100)
)
The line plot shows that in average, the PM2.5, PM10, CO ,and NO2 has higher concentration level at night, and less concentration level at day time.
The Temperature increased since the sun raise and Fridge the maximum at the noon, then decreasing form afternoon to the night
Model fitting
fit decomposition models (monthly)
We are going to find the data to two types of decomposition model. One is the additive decomposition. Another is the multiplicative decomposition. First, we will do the additive decomposition.
# additive decomposition
add_decomp_PM25 <- decompose(ts_by_month[,'PM2.5'], type = 'additive')
add_decomp<- decompose(ts_by_month, type = 'additive')
add_decomp_PM25## $x
## Jan Feb Mar Apr May Jun Jul
## 2013 106.69892 78.82778 81.71640 105.67153 68.14651
## 2014 113.49194 156.06399 98.66667 86.64444 59.18804 58.03889 85.52151
## 2015 103.28199 102.95833 87.32258 71.85556 55.34543 59.44583 61.57124
## 2016 75.26210 48.35201 95.18952 67.05417 55.25806 64.08889 74.10753
## 2017 132.08333 77.61905
## Aug Sep Oct Nov Dec
## 2013 59.41532 61.74306 98.97849 84.30972 92.30914
## 2014 64.41331 70.99903 114.25806 103.31708 67.94247
## 2015 45.68548 53.15000 77.78226 125.42639 165.81989
## 2016 50.55242 59.25139 83.71640 106.37361 156.83468
## 2017
##
## $seasonal
## Jan Feb Mar Apr May Jun
## 2013 12.596727 -5.698226 -24.380240 -21.655511
## 2014 16.017806 21.170881 12.596727 -5.698226 -24.380240 -21.655511
## 2015 16.017806 21.170881 12.596727 -5.698226 -24.380240 -21.655511
## 2016 16.017806 21.170881 12.596727 -5.698226 -24.380240 -21.655511
## 2017 16.017806 21.170881
## Jul Aug Sep Oct Nov Dec
## 2013 -9.601027 -28.952748 -21.657639 13.707981 21.583772 26.868223
## 2014 -9.601027 -28.952748 -21.657639 13.707981 21.583772 26.868223
## 2015 -9.601027 -28.952748 -21.657639 13.707981 21.583772 26.868223
## 2016 -9.601027 -28.952748 -21.657639 13.707981 21.583772 26.868223
## 2017
##
## $trend
## Jan Feb Mar Apr May Jun Jul Aug
## 2013 NA NA NA NA NA NA
## 2014 87.14031 88.07252 88.66643 89.68875 91.11737 90.89406 89.45337 86.81522
## 2015 81.22384 79.44558 77.92155 75.65801 75.05941 80.05886 82.96959 79.52683
## 2016 78.40901 79.13415 79.59116 80.09264 79.54603 78.37778 80.37095 83.95796
## 2017 NA NA
## Sep Oct Nov Dec
## 2013 91.94639 91.93741 91.32442 88.40104
## 2014 84.12981 83.04094 82.26463 82.16314
## 2015 77.57935 77.70708 77.50339 77.69321
## 2016 NA NA NA NA
## 2017
##
## $random
## Jan Feb Mar Apr May
## 2013 NA NA NA
## 2014 10.33382068 46.82059124 -2.59649089 2.65392485 -7.54908995
## 2015 6.04034552 2.34186903 -3.19569409 1.89576779 4.66626068
## 2016 -19.16472204 -51.95301612 3.00162914 -7.34024848 0.09227343
## 2017 NA NA
## Jun Jul Aug Sep Oct
## 2013 NA NA NA -8.54569396 -6.66689181
## 2014 -11.19966299 5.66916168 6.55083331 8.52685202 17.50914281
## 2015 1.04248834 -11.79732274 -4.88859599 -2.77171390 -13.63280684
## 2016 7.36661881 3.33760522 -4.45279316 NA NA
## 2017
## Nov Dec
## 2013 -28.59846862 -22.96012658
## 2014 -0.53131766 -41.08889239
## 2015 26.33923044 61.25846313
## 2016 NA NA
## 2017
##
## $figure
## [1] 12.596727 -5.698226 -24.380240 -21.655511 -9.601027 -28.952748
## [7] -21.657639 13.707981 21.583772 26.868223 16.017806 21.170881
##
## $type
## [1] "additive"
##
## attr(,"class")
## [1] "decomposed.ts"Time series decomposition reduce as four components(Trend,Cycle,Seasonality ,Remainder).
The trend means that the general direction in which the time series is moving.
The cycle is refers to its tendency to rise and fall at inconsistent frequencies.
The seasonal component refers to data that rises and falls at consistent frequencies.
The remainder is means that it exclude trend, cycle, and seasonal components. It is the random fluctuation that cannot explain.
plot(add_decomp_PM25)
In the figure, we can see that the trend overall is declining.The
seasonal component reflecting the fundamental changes in the air
pollutant(PM2.5) since 2014.
add_decomp## $x
## PM2.5 PM10 SO2 NO2 CO O3
## Mar 2013 106.69892 130.19355 41.782387 63.42723 1563.6962 49.67568
## Apr 2013 78.82778 93.94167 22.014413 42.76404 1000.7417 50.78922
## May 2013 81.71640 129.03360 26.635918 52.47490 1094.1250 71.12242
## Jun 2013 105.67153 118.43681 14.815358 52.75863 1628.0139 69.63165
## Jul 2013 68.14651 73.75403 7.801311 45.31321 1223.7702 84.50378
## Aug 2013 59.41532 81.54301 6.996331 45.75652 1075.8065 86.94474
## Sep 2013 61.74306 117.49028 13.512820 57.73660 1326.5194 49.56147
## Oct 2013 98.97849 133.95833 15.550846 73.50200 1392.0699 28.22625
## Nov 2013 84.30972 111.67361 23.508333 58.00556 1575.4167 19.07793
## Dec 2013 92.30914 121.84812 44.816955 66.48069 2213.8441 12.87716
## Jan 2014 113.49194 152.32863 61.379032 79.61559 2171.3710 12.22043
## Feb 2014 156.06399 176.36310 67.059524 74.99405 2458.0357 18.06548
## Mar 2014 98.66667 157.95161 40.067204 66.39785 1489.1129 47.58333
## Apr 2014 86.64444 141.04306 18.758333 54.85417 1075.8333 68.79861
## May 2014 59.18804 112.96250 14.621640 47.10403 934.5430 92.11142
## Jun 2014 58.03889 81.15000 6.341667 46.40833 990.5556 103.63750
## Jul 2014 85.52151 110.45161 5.244624 40.52151 907.9301 104.85215
## Aug 2014 64.41331 91.18616 4.044624 49.18696 1027.1505 94.55497
## Sep 2014 70.99903 97.71708 5.679167 59.13194 1162.5000 53.78361
## Oct 2014 114.25806 143.46505 8.204301 76.72177 1372.3118 26.74059
## Nov 2014 103.31708 142.29014 14.245139 77.05292 1785.4167 22.32083
## Dec 2014 67.94247 111.75591 33.370027 63.90403 1873.9247 29.50847
## Jan 2015 103.28199 128.48925 39.075672 76.75376 2011.6935 24.22755
## Feb 2015 102.95833 133.78869 29.120536 59.45833 1557.1429 38.70536
## Mar 2015 87.32258 155.15323 23.263441 59.77419 1257.3925 54.28763
## Apr 2015 71.85556 121.17083 9.693056 49.62222 835.8333 78.03472
## May 2015 55.34543 93.78898 9.059140 41.90726 779.1667 98.06855
## Jun 2015 59.44583 81.00139 6.877778 37.44861 865.8333 92.75417
## Jul 2015 61.57124 77.40188 4.935484 38.15995 978.3602 95.05780
## Aug 2015 45.68548 67.98118 3.108871 35.40726 909.6774 100.36694
## Sep 2015 53.15000 68.63472 4.965278 43.25139 956.6667 58.35278
## Oct 2015 77.78226 98.78629 5.424731 55.75672 1043.9516 36.92473
## Nov 2015 125.42639 131.26806 14.548611 60.19444 2085.4167 14.15139
## Dec 2015 165.81989 175.36425 24.176075 73.86290 3024.3280 17.96102
## Jan 2016 75.26210 88.44892 24.372312 52.94892 1639.1129 28.16935
## Feb 2016 48.35201 61.49856 17.149425 34.41810 933.9080 47.92385
## Mar 2016 95.18952 130.83737 20.548387 53.99194 1223.9247 48.20565
## Apr 2016 67.05417 109.42500 11.688889 41.57083 852.0833 72.54167
## May 2016 55.25806 95.65995 9.151882 37.45833 724.3280 99.22043
## Jun 2016 64.08889 82.17778 5.462500 34.99444 865.8333 126.60556
## Jul 2016 74.10753 82.06452 3.322581 34.48925 997.9839 96.86290
## Aug 2016 50.55242 64.67608 2.659946 39.72849 932.6613 76.13575
## Sep 2016 59.25139 70.65417 2.827778 50.75833 870.1389 56.39444
## Oct 2016 83.71640 94.86962 3.310484 61.01210 1246.5054 20.25538
## Nov 2016 106.37361 136.37778 10.468056 71.47778 1812.7778 14.05556
## Dec 2016 156.83468 169.18011 17.418011 89.91532 2604.1667 15.15188
## Jan 2017 132.08333 149.47984 18.594086 71.23522 2254.3011 27.93952
## Feb 2017 77.61905 90.79464 18.520833 56.49405 1173.6607 40.98810
## TEMP PRES DEWP RAIN WSPM
## Mar 2013 6.373252688 1011.6395 -6.3188172 0.0236559140 1.753495
## Apr 2013 12.599166667 1007.2869 -2.8651389 0.0141666667 2.223472
## May 2013 21.787903226 1002.1239 8.4520161 0.0076612903 1.771237
## Jun 2013 23.783055556 999.0772 17.5343056 0.1015277778 1.355000
## Jul 2013 27.156451613 995.0235 21.1831989 0.2802419355 1.359946
## Aug 2013 27.257661290 998.2694 20.0935484 0.0907258065 1.416398
## Sep 2013 20.487361111 1008.3138 14.5504167 0.1150000000 1.160972
## Oct 2013 13.199865591 1015.2367 5.3115591 0.0170698925 1.337366
## Nov 2013 5.880555556 1016.0646 -7.1959722 0.0008333333 1.769028
## Dec 2013 -0.005241935 1019.1534 -13.2763441 0.0000000000 1.699866
## Jan 2014 0.173655914 1019.2828 -12.6904570 0.0000000000 1.618548
## Feb 2014 0.089434524 1021.6240 -9.5802083 0.0098214286 1.438244
## Mar 2014 10.513844086 1012.8694 -5.8724462 0.0001344086 1.810215
## Apr 2014 17.184027778 1009.5782 3.9636111 0.0180555556 1.615556
## May 2014 21.865188172 1000.7228 6.9375000 0.0915322581 2.020027
## Jun 2014 24.901944444 999.3411 16.3420833 0.1980555556 1.393472
## Jul 2014 28.287634409 997.8254 19.5525538 0.0581989247 1.479973
## Aug 2014 26.208736559 1001.8782 18.1295699 0.1381720430 1.395833
## Sep 2014 21.123472222 1007.9142 13.8113889 0.0547222222 1.310833
## Oct 2014 14.044892473 1013.6585 6.2706989 0.0182795699 1.217070
## Nov 2014 6.371111111 1021.8025 -5.1972222 0.0004166667 1.538472
## Dec 2014 -0.226478495 1025.9004 -16.1875000 0.0000000000 2.189113
## Jan 2015 -0.125537634 1020.9488 -13.7850806 0.0005376344 1.604704
## Feb 2015 1.743154762 1017.6015 -12.4601190 0.0168154762 1.811905
## Mar 2015 8.439861751 1016.8734 -9.8809140 0.0088709677 2.213575
## Apr 2015 15.630138889 1010.8733 1.6945833 0.0556944444 2.483056
## May 2015 21.455510753 1003.4489 6.6134409 0.0501344086 2.471102
## Jun 2015 24.537777778 1000.3461 14.3013889 0.1362500000 1.980278
## Jul 2015 26.397849462 1001.2784 18.5057796 0.2701612903 1.627285
## Aug 2015 26.435752688 1003.4042 18.4461022 0.1258064516 1.615457
## Sep 2015 20.600833333 1011.3549 13.7698611 0.1372222222 1.601944
## Oct 2015 14.319758065 1015.7254 4.1530914 0.0190860215 1.848790
## Nov 2015 2.847777778 1023.4250 -1.2023611 0.0522222222 1.548056
## Dec 2015 -0.362768817 1024.0706 -7.2271505 0.0028225806 1.856452
## Jan 2016 -4.550000000 1025.9500 -18.0596774 0.0006720430 2.115054
## Feb 2016 1.398419540 1022.5598 -15.0882184 0.0181034483 2.449138
## Mar 2016 9.201881720 1016.7401 -8.7526882 0.0000000000 2.049866
## Apr 2016 16.454722222 1007.8117 -0.3329167 0.0066666667 2.382361
## May 2016 21.672849462 1005.5414 6.2018817 0.0458333333 2.207796
## Jun 2016 25.735833333 1000.7619 14.6834722 0.0991666667 1.803056
## Jul 2016 27.699462366 1000.6353 20.7272849 0.4233870968 1.698925
## Aug 2016 27.863306452 1003.5901 19.2868280 0.0724462366 1.618414
## Sep 2016 22.197344026 1009.3406 14.0559722 0.1598611111 1.554444
## Oct 2016 13.338648073 1017.1267 7.2780914 0.1174731183 1.476882
## Nov 2016 4.414027778 1020.5669 -3.7584722 0.0073611111 1.557778
## Dec 2016 0.640725806 1023.4661 -9.2724462 0.0000000000 1.435618
## Jan 2017 -1.140412186 1025.0380 -12.7756720 0.0004032258 1.969220
## Feb 2017 2.661532738 1022.0206 -13.6276786 0.0061011905 1.953869
##
## $seasonal
## Jan Feb Mar Apr May Jun
## 2013 3.998767 -34.759863 -46.821312 -39.493936
## 2014 55.312609 29.866751 3.998767 -34.759863 -46.821312 -39.493936
## 2015 55.312609 29.866751 3.998767 -34.759863 -46.821312 -39.493936
## 2016 55.312609 29.866751 3.998767 -34.759863 -46.821312 -39.493936
## 2017 55.312609 29.866751 3.998767 -34.759863 -46.821312 -39.493936
## 2018 55.312609 29.866751 3.998767 -34.759863 -46.821312 -39.493936
## 2019 55.312609 29.866751 3.998767 -34.759863 -46.821312 -39.493936
## 2020 55.312609 29.866751 3.998767 -34.759863 -46.821312 -39.493936
## 2021 55.312609 29.866751 3.998767 -34.759863 -46.821312 -39.493936
## 2022 55.312609 29.866751 3.998767 -34.759863 -46.821312 -39.493936
## 2023 55.312609 29.866751 3.998767 -34.759863 -46.821312 -39.493936
## 2024 55.312609 29.866751 3.998767 -34.759863 -46.821312 -39.493936
## 2025 55.312609 29.866751 3.998767 -34.759863 -46.821312 -39.493936
## 2026 55.312609 29.866751 3.998767 -34.759863 -46.821312 -39.493936
## 2027 55.312609 29.866751 3.998767 -34.759863 -46.821312 -39.493936
## 2028 55.312609 29.866751 3.998767 -34.759863 -46.821312 -39.493936
## 2029 55.312609 29.866751 3.998767 -34.759863 -46.821312 -39.493936
## 2030 55.312609 29.866751 3.998767 -34.759863 -46.821312 -39.493936
## 2031 55.312609 29.866751 3.998767 -34.759863 -46.821312 -39.493936
## 2032 55.312609 29.866751 3.998767 -34.759863 -46.821312 -39.493936
## 2033 55.312609 29.866751 3.998767 -34.759863 -46.821312 -39.493936
## 2034 55.312609 29.866751 3.998767 -34.759863 -46.821312 -39.493936
## 2035 55.312609 29.866751 3.998767 -34.759863 -46.821312 -39.493936
## 2036 55.312609 29.866751 3.998767 -34.759863 -46.821312 -39.493936
## 2037 55.312609 29.866751 3.998767 -34.759863 -46.821312 -39.493936
## 2038 55.312609 29.866751 3.998767 -34.759863 -46.821312 -39.493936
## 2039 55.312609 29.866751 3.998767 -34.759863 -46.821312 -39.493936
## 2040 55.312609 29.866751 3.998767 -34.759863 -46.821312 -39.493936
## 2041 55.312609 29.866751 3.998767 -34.759863 -46.821312 -39.493936
## 2042 55.312609 29.866751 3.998767 -34.759863 -46.821312 -39.493936
## 2043 55.312609 29.866751 3.998767 -34.759863 -46.821312 -39.493936
## 2044 55.312609 29.866751 3.998767 -34.759863 -46.821312 -39.493936
## 2045 55.312609 29.866751 3.998767 -34.759863 -46.821312 -39.493936
## 2046 55.312609 29.866751 3.998767 -34.759863 -46.821312 -39.493936
## 2047 55.312609 29.866751 3.998767 -34.759863 -46.821312 -39.493936
## 2048 55.312609 29.866751 3.998767 -34.759863 -46.821312 -39.493936
## 2049 55.312609 29.866751 3.998767 -34.759863 -46.821312 -39.493936
## 2050 55.312609 29.866751 3.998767 -34.759863 -46.821312 -39.493936
## 2051 55.312609 29.866751 3.998767 -34.759863 -46.821312 -39.493936
## 2052 55.312609 29.866751 3.998767 -34.759863 -46.821312 -39.493936
## 2053 55.312609 29.866751 3.998767 -34.759863 -46.821312 -39.493936
## 2054 55.312609 29.866751 3.998767 -34.759863 -46.821312 -39.493936
## 2055 55.312609 29.866751 3.998767 -34.759863 -46.821312 -39.493936
## 2056 55.312609 29.866751 3.998767 -34.759863 -46.821312 -39.493936
## 2057 55.312609 29.866751
## Jul Aug Sep Oct Nov Dec
## 2013 -33.856298 -36.175662 -24.854130 -8.723305 40.661334 94.845043
## 2014 -33.856298 -36.175662 -24.854130 -8.723305 40.661334 94.845043
## 2015 -33.856298 -36.175662 -24.854130 -8.723305 40.661334 94.845043
## 2016 -33.856298 -36.175662 -24.854130 -8.723305 40.661334 94.845043
## 2017 -33.856298 -36.175662 -24.854130 -8.723305 40.661334 94.845043
## 2018 -33.856298 -36.175662 -24.854130 -8.723305 40.661334 94.845043
## 2019 -33.856298 -36.175662 -24.854130 -8.723305 40.661334 94.845043
## 2020 -33.856298 -36.175662 -24.854130 -8.723305 40.661334 94.845043
## 2021 -33.856298 -36.175662 -24.854130 -8.723305 40.661334 94.845043
## 2022 -33.856298 -36.175662 -24.854130 -8.723305 40.661334 94.845043
## 2023 -33.856298 -36.175662 -24.854130 -8.723305 40.661334 94.845043
## 2024 -33.856298 -36.175662 -24.854130 -8.723305 40.661334 94.845043
## 2025 -33.856298 -36.175662 -24.854130 -8.723305 40.661334 94.845043
## 2026 -33.856298 -36.175662 -24.854130 -8.723305 40.661334 94.845043
## 2027 -33.856298 -36.175662 -24.854130 -8.723305 40.661334 94.845043
## 2028 -33.856298 -36.175662 -24.854130 -8.723305 40.661334 94.845043
## 2029 -33.856298 -36.175662 -24.854130 -8.723305 40.661334 94.845043
## 2030 -33.856298 -36.175662 -24.854130 -8.723305 40.661334 94.845043
## 2031 -33.856298 -36.175662 -24.854130 -8.723305 40.661334 94.845043
## 2032 -33.856298 -36.175662 -24.854130 -8.723305 40.661334 94.845043
## 2033 -33.856298 -36.175662 -24.854130 -8.723305 40.661334 94.845043
## 2034 -33.856298 -36.175662 -24.854130 -8.723305 40.661334 94.845043
## 2035 -33.856298 -36.175662 -24.854130 -8.723305 40.661334 94.845043
## 2036 -33.856298 -36.175662 -24.854130 -8.723305 40.661334 94.845043
## 2037 -33.856298 -36.175662 -24.854130 -8.723305 40.661334 94.845043
## 2038 -33.856298 -36.175662 -24.854130 -8.723305 40.661334 94.845043
## 2039 -33.856298 -36.175662 -24.854130 -8.723305 40.661334 94.845043
## 2040 -33.856298 -36.175662 -24.854130 -8.723305 40.661334 94.845043
## 2041 -33.856298 -36.175662 -24.854130 -8.723305 40.661334 94.845043
## 2042 -33.856298 -36.175662 -24.854130 -8.723305 40.661334 94.845043
## 2043 -33.856298 -36.175662 -24.854130 -8.723305 40.661334 94.845043
## 2044 -33.856298 -36.175662 -24.854130 -8.723305 40.661334 94.845043
## 2045 -33.856298 -36.175662 -24.854130 -8.723305 40.661334 94.845043
## 2046 -33.856298 -36.175662 -24.854130 -8.723305 40.661334 94.845043
## 2047 -33.856298 -36.175662 -24.854130 -8.723305 40.661334 94.845043
## 2048 -33.856298 -36.175662 -24.854130 -8.723305 40.661334 94.845043
## 2049 -33.856298 -36.175662 -24.854130 -8.723305 40.661334 94.845043
## 2050 -33.856298 -36.175662 -24.854130 -8.723305 40.661334 94.845043
## 2051 -33.856298 -36.175662 -24.854130 -8.723305 40.661334 94.845043
## 2052 -33.856298 -36.175662 -24.854130 -8.723305 40.661334 94.845043
## 2053 -33.856298 -36.175662 -24.854130 -8.723305 40.661334 94.845043
## 2054 -33.856298 -36.175662 -24.854130 -8.723305 40.661334 94.845043
## 2055 -33.856298 -36.175662 -24.854130 -8.723305 40.661334 94.845043
## 2056 -33.856298 -36.175662 -24.854130 -8.723305 40.661334 94.845043
## 2057
##
## $trend
## [,1] [,2] [,3] [,4] [,5] [,6] [,7]
## Mar 2013 NA NA NA NA NA NA NA
## Apr 2013 NA NA NA NA NA NA NA
## May 2013 NA NA NA NA NA NA NA
## Jun 2013 NA NA NA NA NA NA NA
## Jul 2013 NA NA NA NA NA NA NA
## Aug 2013 NA NA NA NA NA NA NA
## Sep 2013 91.94639 121.20365 28.75130 59.52619 1557.177 45.97084 13.40445
## Oct 2013 91.93741 124.32279 28.54417 60.15372 1557.198 46.63405 13.76801
## Nov 2013 91.32442 125.61572 27.90790 60.43369 1553.677 48.25898 13.96227
## Dec 2013 88.40104 123.39247 27.05424 59.94531 1520.467 50.55043 14.01211
## Jan 2014 87.14031 123.36792 26.59464 59.48106 1480.747 52.81519 14.10586
## Feb 2014 88.07252 125.29879 26.36512 59.42434 1465.559 53.98013 14.10929
## Mar 2014 88.66643 124.87670 25.91573 59.62542 1456.698 54.47315 14.09209
## Apr 2014 89.68875 124.44893 25.28322 59.81771 1449.040 54.58717 14.15380
## May 2014 91.11737 126.12073 24.59115 60.74551 1456.967 54.66039 14.20945
## Jun 2014 90.89406 126.97591 23.72823 61.43179 1451.554 55.48848 14.22067
## Jul 2014 89.45337 125.56210 22.32197 61.20519 1430.737 56.68175 14.19899
## Aug 2014 86.81522 122.79486 19.81187 60.43862 1386.547 58.04204 14.25543
## Sep 2014 84.12981 120.90432 17.53092 59.51532 1339.355 59.18138 14.23792
## Oct 2014 83.04094 119.95971 16.45304 59.02133 1319.700 59.84556 14.08676
## Nov 2014 82.26463 118.33281 15.84355 58.58680 1303.226 60.47862 14.00494
## Dec 2014 82.16314 117.52772 15.63412 57.99695 1291.555 60.27336 13.97270
## Jan 2015 81.22384 116.14445 15.64358 57.52523 1289.293 59.41179 13.87878
## Feb 2015 79.44558 113.80051 15.59171 56.85268 1287.332 59.24585 13.80950
## Mar 2015 77.92155 111.62187 15.52297 55.61683 1273.861 59.67840 13.79718
## Apr 2015 75.65801 108.54849 15.37741 54.08160 1251.603 60.29312 13.78686
## May 2015 75.05941 106.22762 15.27424 52.50562 1250.422 60.37707 13.65151
## Jun 2015 80.05886 108.41871 14.90380 52.21813 1310.855 59.55553 13.49902
## Jul 2015 82.96959 109.40072 13.90808 51.64122 1343.264 59.23863 13.30899
## Aug 2015 79.52683 104.72028 12.79665 49.60601 1301.772 59.78697 13.11027
## Sep 2015 77.57935 100.69503 12.18472 48.32174 1274.409 59.91766 13.12766
## Oct 2015 77.70708 99.19246 12.15476 47.74534 1273.692 59.43537 13.19377
## Nov 2015 77.50339 98.78101 12.24178 47.22449 1272.084 59.25449 13.23718
## Dec 2015 77.69321 98.90798 12.18667 46.93686 1269.799 60.71295 13.29616
## Jan 2016 78.40901 99.15127 12.06050 46.68166 1270.617 62.19864 13.40031
## Feb 2016 79.13415 99.20784 11.97459 46.70876 1272.392 61.26422 13.51402
## Mar 2016 79.59116 99.15427 11.86682 47.20160 1269.745 60.17299 13.64003
## Apr 2016 80.09264 99.07522 11.68967 47.73337 1274.579 59.39684 13.66567
## May 2016 79.54603 99.12493 11.43155 48.42248 1271.659 58.69829 13.69005
## Jun 2016 78.37778 99.08016 10.97994 49.56147 1242.792 58.57725 13.79712
## Jul 2016 80.37095 101.36544 10.45759 50.99225 1250.918 58.45062 13.98100
## Aug 2016 83.95796 105.12907 10.27398 52.67401 1286.541 58.15206 14.17570
## Sep 2016 NA NA NA NA NA NA NA
## Oct 2016 NA NA NA NA NA NA NA
## Nov 2016 NA NA NA NA NA NA NA
## Dec 2016 NA NA NA NA NA NA NA
## Jan 2017 NA NA NA NA NA NA NA
## Feb 2017 NA NA NA NA NA NA NA
## [,8] [,9] [,10] [,11]
## Mar 2013 NA NA NA NA
## Apr 2013 NA NA NA NA
## May 2013 NA NA NA NA
## Jun 2013 NA NA NA NA
## Jul 2013 NA NA NA NA
## Aug 2013 NA NA NA NA
## Sep 2013 1009.476 2.951774 0.05407861 1.577661
## Oct 2013 1009.623 3.254904 0.05326058 1.554694
## Nov 2013 1009.660 3.476331 0.05691724 1.539731
## Dec 2013 1009.612 3.363550 0.06443386 1.551700
## Jan 2014 1009.740 3.245931 0.05920406 1.558304
## Feb 2014 1010.007 3.096155 0.05192919 1.562449
## Mar 2014 1010.141 2.983529 0.05139454 1.567836
## Apr 2014 1010.058 2.992701 0.04893337 1.569068
## May 2014 1010.232 3.115946 0.04896641 1.554449
## Jun 2014 1010.752 3.077929 0.04894905 1.565228
## Jul 2014 1011.103 2.911022 0.04897145 1.585036
## Aug 2014 1011.004 2.745416 0.04928527 1.600029
## Sep 2014 1011.004 2.458400 0.04994072 1.632404
## Oct 2014 1011.224 2.196838 0.05187303 1.685357
## Nov 2014 1011.392 2.088793 0.05171640 1.740298
## Dec 2014 1011.547 1.990261 0.04741626 1.783543
## Jan 2015 1011.733 1.861617 0.05367280 1.814131
## Feb 2015 1011.941 1.831190 0.06198933 1.829420
## Mar 2015 1012.148 1.842649 0.06491159 1.850700
## Apr 2015 1012.377 1.752685 0.06838270 1.889152
## May 2015 1012.531 1.830903 0.07057486 1.915873
## Jun 2015 1012.522 2.370704 0.07285104 1.902411
## Jul 2015 1012.654 2.565944 0.07297424 1.909815
## Aug 2015 1013.069 2.278331 0.07303351 1.957631
## Sep 2015 1013.270 2.215837 0.07271755 1.977361
## Oct 2015 1013.137 2.178367 0.07030510 1.966344
## Nov 2015 1013.097 2.076739 0.06808307 1.951177
## Dec 2015 1013.201 2.075511 0.06635872 1.932822
## Jan 2016 1013.192 2.183994 0.07119799 1.928423
## Feb 2016 1013.173 2.311587 0.07535905 1.931531
## Mar 2016 1013.097 2.358539 0.07407900 1.929675
## Apr 2016 1013.071 2.500668 0.07912175 1.912200
## May 2016 1013.010 2.524372 0.08135200 1.897109
## Jun 2016 1012.866 2.332647 0.07936518 1.879979
## Jul 2016 1012.803 2.467593 0.07923637 1.856368
## Aug 2016 1012.742 2.748616 0.07872507 1.829655
## Sep 2016 NA NA NA NA
## Oct 2016 NA NA NA NA
## Nov 2016 NA NA NA NA
## Dec 2016 NA NA NA NA
## Jan 2017 NA NA NA NA
## Feb 2017 NA NA NA NA
##
## $random
## x - seasonal.x.PM2.5 x - seasonal.x.PM10 x - seasonal.x.SO2
## Mar 2013 NA NA NA
## Apr 2013 NA NA NA
## May 2013 NA NA NA
## Jun 2013 NA NA NA
## Jul 2013 NA NA NA
## Aug 2013 NA NA NA
## Sep 2013 -5.349203 21.1407608 9.6156468
## Oct 2013 15.764394 18.3588480 -4.2700155
## Nov 2013 -47.676030 -54.6034424 -45.0609031
## Dec 2013 -90.936947 -96.3893983 -77.0823253
## Jan 2014 -28.960982 -26.3519018 -20.5282141
## Feb 2014 38.124721 21.1975582 10.8276512
## Mar 2014 6.001469 29.0761455 10.1527061
## Apr 2014 31.715562 51.3539876 28.2349730
## May 2014 14.891982 33.6630789 36.8518008
## Jun 2014 6.638761 -6.3319773 22.1073734
## Jul 2014 29.924432 18.7458137 16.7789545
## Aug 2014 13.773747 4.5669619 20.4084164
## Sep 2014 11.723343 1.6668906 13.0023757
## Oct 2014 39.940429 32.2286453 0.4745623
## Nov 2014 -19.608879 -16.7040032 -42.2597487
## Dec 2014 -109.065713 -100.6168484 -77.1091370
## Jan 2015 -33.254457 -42.9678161 -31.8805143
## Feb 2015 -6.354002 -9.8785696 -16.3379228
## Mar 2015 5.402266 39.5325890 3.7417018
## Apr 2015 30.957405 47.3822063 29.0755069
## May 2015 27.107332 34.3826690 40.6062107
## Jun 2015 18.880913 12.0766096 31.4679093
## Jul 2015 12.457948 1.8574640 24.8836988
## Aug 2015 2.334318 -0.5634354 26.4878862
## Sep 2015 0.424777 -7.2061782 17.6346848
## Oct 2015 8.798479 8.3171360 1.9932813
## Nov 2015 7.261669 -8.1742857 -38.3545024
## Dec 2015 -6.718357 -18.3887762 -82.8556417
## Jan 2016 -58.459524 -66.0149568 -43.0007962
## Feb 2016 -60.648887 -67.5760246 -24.6919160
## Mar 2016 11.599589 27.6843314 4.6827979
## Apr 2016 21.721389 45.1096464 34.7590854
## May 2016 22.533345 43.3563308 44.5416439
## Jun 2016 25.205043 22.5915538 33.9764954
## Jul 2016 27.592876 14.5553719 26.7212835
## Aug 2016 2.770121 -4.2773296 28.5616305
## Sep 2016 NA NA NA
## Oct 2016 NA NA NA
## Nov 2016 NA NA NA
## Dec 2016 NA NA NA
## Jan 2017 NA NA NA
## Feb 2017 NA NA NA
## x - seasonal.x.NO2 x - seasonal.x.CO x - seasonal.x.O3
## Mar 2013 NA NA NA
## Apr 2013 NA NA NA
## May 2013 NA NA NA
## Jun 2013 NA NA NA
## Jul 2013 NA NA NA
## Aug 2013 NA NA NA
## Sep 2013 23.0645354 -205.80297 28.444759
## Oct 2013 22.0715805 -156.40453 -9.684491
## Nov 2013 -43.0894713 -18.92196 -69.842382
## Dec 2013 -88.3096672 598.53176 -132.518312
## Jan 2014 -35.1780781 635.31185 -95.907370
## Feb 2014 -14.2970456 962.60978 -65.781408
## Mar 2014 2.7736658 28.41643 -10.888582
## Apr 2014 29.7963159 -338.44712 48.971305
## May 2014 33.1798330 -475.60274 84.272349
## Jun 2014 24.4704786 -421.50426 87.642956
## Jul 2014 13.1726161 -488.95082 82.026701
## Aug 2014 24.9240014 -323.22059 72.688596
## Sep 2014 24.4707589 -152.00044 19.456361
## Oct 2014 26.4237475 61.33558 -24.381667
## Nov 2014 -22.1952197 441.52979 -78.819116
## Dec 2014 -88.9379592 487.52492 -125.609932
## Jan 2015 -36.0840733 667.08835 -90.496841
## Feb 2015 -27.2610934 239.94364 -50.407247
## Mar 2015 0.1585953 -20.46766 -9.389533
## Apr 2015 30.3004873 -381.01011 52.501464
## May 2015 36.2229523 -424.43365 84.512793
## Jun 2015 24.7244127 -405.52783 72.692573
## Jul 2015 20.3750252 -331.04786 69.675465
## Aug 2015 21.9769122 -355.91898 76.755624
## Sep 2015 19.7837817 -292.88866 23.289247
## Oct 2015 16.7346907 -221.01713 -13.787331
## Nov 2015 -27.6913785 772.67115 -85.764431
## Dec 2015 -67.9190000 1659.68368 -137.596977
## Jan 2016 -49.0453411 313.18341 -89.341896
## Feb 2016 -42.1574108 -368.35091 -43.207123
## Mar 2016 2.7915647 -49.81858 -15.966114
## Apr 2016 28.5973288 -387.73576 47.904690
## May 2016 35.8571648 -500.50947 87.343452
## Jun 2016 24.9269102 -337.46480 107.522242
## Jul 2016 17.3532955 -219.07802 72.268576
## Aug 2016 23.2301471 -317.70377 54.159356
## Sep 2016 NA NA NA
## Oct 2016 NA NA NA
## Nov 2016 NA NA NA
## Dec 2016 NA NA NA
## Jan 2017 NA NA NA
## Feb 2017 NA NA NA
## x - seasonal.x.TEMP x - seasonal.x.PRES x - seasonal.x.DEWP
## Mar 2013 NA NA NA
## Apr 2013 NA NA NA
## May 2013 NA NA NA
## Jun 2013 NA NA NA
## Jul 2013 NA NA NA
## Aug 2013 NA NA NA
## Sep 2013 31.937040 23.6920012 36.45277
## Oct 2013 8.155159 14.3374083 10.77996
## Nov 2013 -48.743047 -34.2564322 -51.33364
## Dec 2013 -108.862394 -85.3039816 -111.48494
## Jan 2014 -69.244814 -45.7698519 -71.24900
## Feb 2014 -43.886606 -18.2499467 -42.54311
## Mar 2014 -7.577011 -1.2702862 -12.85474
## Apr 2014 37.790088 34.2795918 35.73077
## May 2014 54.477048 37.3123752 50.64287
## Jun 2014 50.175207 28.0830542 52.75809
## Jul 2014 47.944943 20.5791651 50.49783
## Aug 2014 48.128971 27.0495383 51.55982
## Sep 2014 31.739686 21.7647147 36.20712
## Oct 2014 8.681443 11.1573916 12.79717
## Nov 2014 -48.295163 -30.2507663 -47.94735
## Dec 2014 -109.044218 -80.4920337 -113.02280
## Jan 2015 -69.316928 -46.0969601 -70.95931
## Feb 2015 -41.933096 -24.2058591 -44.15806
## Mar 2015 -9.356087 0.7271035 -15.72233
## Apr 2015 36.603143 33.2561724 34.70176
## May 2015 54.625317 37.7394862 51.60385
## Jun 2015 50.532692 27.3179356 51.42462
## Jul 2015 46.945157 22.4804063 49.79613
## Aug 2015 49.501141 26.5105980 52.34343
## Sep 2015 32.327303 22.9387221 36.40815
## Oct 2015 9.849295 11.3115657 10.69803
## Nov 2015 -51.050738 -30.3330940 -43.94043
## Dec 2015 -108.503969 -83.9757514 -104.14771
## Jan 2016 -73.262918 -42.5544155 -75.55628
## Feb 2016 -41.982357 -20.4797413 -47.26656
## Mar 2016 -8.436913 -0.3552892 -15.10999
## Apr 2016 37.548916 29.5004957 31.92628
## May 2016 54.804111 39.3523744 50.49882
## Jun 2016 51.432646 27.3898155 51.84476
## Jul 2016 47.574759 21.6887686 52.11599
## Aug 2016 49.863271 27.0233042 52.71387
## Sep 2016 NA NA NA
## Oct 2016 NA NA NA
## Nov 2016 NA NA NA
## Dec 2016 NA NA NA
## Jan 2017 NA NA NA
## Feb 2017 NA NA NA
## x - seasonal.x.RAIN x - seasonal.x.WSPM
## Mar 2013 NA NA
## Apr 2013 NA NA
## May 2013 NA NA
## Jun 2013 NA NA
## Jul 2013 NA NA
## Aug 2013 NA NA
## Sep 2013 24.915051 24.437441
## Oct 2013 8.687115 8.505977
## Nov 2013 -40.717418 -40.432037
## Dec 2013 -94.909477 -94.696878
## Jan 2014 -55.371813 -55.252364
## Feb 2014 -29.908859 -29.990956
## Mar 2014 -4.050027 -3.756388
## Apr 2014 34.728985 34.806350
## May 2014 46.863877 47.286889
## Jun 2014 39.643042 39.322180
## Jul 2014 33.865525 33.751234
## Aug 2014 36.264548 35.971466
## Sep 2014 24.858911 24.532559
## Oct 2014 8.689712 8.255018
## Nov 2014 -40.712634 -40.863160
## Dec 2014 -94.892460 -94.439473
## Jan 2015 -55.365744 -55.522035
## Feb 2015 -29.911925 -29.884266
## Mar 2015 -4.054808 -3.635892
## Apr 2015 34.747174 35.353766
## May 2015 46.800871 47.376541
## Jun 2015 39.557334 39.571802
## Jul 2015 34.053485 33.573768
## Aug 2015 36.228435 35.833488
## Sep 2015 24.918635 24.478713
## Oct 2015 8.672086 8.605752
## Nov 2015 -40.677195 -41.064456
## Dec 2015 -94.908579 -94.921414
## Jan 2016 -55.383135 -55.125978
## Feb 2016 -29.924007 -29.349144
## Mar 2016 -4.072846 -3.878576
## Apr 2016 34.687408 35.230024
## May 2016 46.785793 47.131999
## Jun 2016 39.513737 39.417012
## Jul 2016 34.200448 33.698854
## Aug 2016 36.169383 35.964420
## Sep 2016 NA NA
## Oct 2016 NA NA
## Nov 2016 NA NA
## Dec 2016 NA NA
## Jan 2017 NA NA
## Feb 2017 NA NA
##
## $figure
## [1] 3.998767 -34.759863 -46.821312 -39.493936 -33.856298 -36.175662
## [7] -24.854130 -8.723305 40.661334 94.845043 55.312609 29.866751
##
## $type
## [1] "additive"
##
## attr(,"class")
## [1] "decomposed.ts"We can observe the fundamental changes of different air pollutants and weather conditions in 2014 to 2017.
plot(add_decomp$x[,1:6])
plot(add_decomp$x[,7:11])
We also check the fundamental changes in the four components(Trend,Cycle,Seasonality ,Remainder) in 2014 to 2017.
For example, in seasonal, we can check that is the fundamental changes similar in different seasons. And we found that there are similar pattern in the figure in different period.
Moreover, in the trend, we can check the general direction in the time series in 2014 to 2017. For example, we found that the trend of SO2 shows a remarkable decline since 2014.
plot(add_decomp$seasonal[1:60], type = "l")
plot(add_decomp$trend[,1:6])
plot(add_decomp$trend[,7:11])
plot(add_decomp$random[,1:6])
plot(add_decomp$random[,7:11])
multiplicative decomposition
Second, we will do the multiplicative decomposition.
multi_decomp_PM25 <- decompose(ts_by_month[,'PM2.5'], type = 'multiplicative')
multi_decomp <- decompose(ts_by_month, type = 'multiplicative')
multi_decomp_PM25## $x
## Jan Feb Mar Apr May Jun Jul
## 2013 106.69892 78.82778 81.71640 105.67153 68.14651
## 2014 113.49194 156.06399 98.66667 86.64444 59.18804 58.03889 85.52151
## 2015 103.28199 102.95833 87.32258 71.85556 55.34543 59.44583 61.57124
## 2016 75.26210 48.35201 95.18952 67.05417 55.25806 64.08889 74.10753
## 2017 132.08333 77.61905
## Aug Sep Oct Nov Dec
## 2013 59.41532 61.74306 98.97849 84.30972 92.30914
## 2014 64.41331 70.99903 114.25806 103.31708 67.94247
## 2015 45.68548 53.15000 77.78226 125.42639 165.81989
## 2016 50.55242 59.25139 83.71640 106.37361 156.83468
## 2017
##
## $seasonal
## Jan Feb Mar Apr May Jun Jul
## 2013 1.1536745 0.9261272 0.7002633 0.7396729 0.8814532
## 2014 1.1888050 1.2376261 1.1536745 0.9261272 0.7002633 0.7396729 0.8814532
## 2015 1.1888050 1.2376261 1.1536745 0.9261272 0.7002633 0.7396729 0.8814532
## 2016 1.1888050 1.2376261 1.1536745 0.9261272 0.7002633 0.7396729 0.8814532
## 2017 1.1888050 1.2376261
## Aug Sep Oct Nov Dec
## 2013 0.6454082 0.7402740 1.1617698 1.2774791 1.3474468
## 2014 0.6454082 0.7402740 1.1617698 1.2774791 1.3474468
## 2015 0.6454082 0.7402740 1.1617698 1.2774791 1.3474468
## 2016 0.6454082 0.7402740 1.1617698 1.2774791 1.3474468
## 2017
##
## $trend
## Jan Feb Mar Apr May Jun Jul Aug
## 2013 NA NA NA NA NA NA
## 2014 87.14031 88.07252 88.66643 89.68875 91.11737 90.89406 89.45337 86.81522
## 2015 81.22384 79.44558 77.92155 75.65801 75.05941 80.05886 82.96959 79.52683
## 2016 78.40901 79.13415 79.59116 80.09264 79.54603 78.37778 80.37095 83.95796
## 2017 NA NA
## Sep Oct Nov Dec
## 2013 91.94639 91.93741 91.32442 88.40104
## 2014 84.12981 83.04094 82.26463 82.16314
## 2015 77.57935 77.70708 77.50339 77.69321
## 2016 NA NA NA NA
## 2017
##
## $random
## Jan Feb Mar Apr May Jun Jul
## 2013 NA NA NA NA NA
## 2014 1.0955578 1.4317686 0.9645571 1.0431149 0.9276228 0.8632645 1.0846244
## 2015 1.0696223 1.0471341 0.9713723 1.0254979 1.0529682 1.0038581 0.8418984
## 2016 0.8074204 0.4936978 1.0366711 0.9039877 0.9920094 1.1054779 1.0460777
## 2017 NA NA
## Aug Sep Oct Nov Dec
## 2013 NA 0.9071121 0.9266773 0.7226649 0.7749536
## 2014 1.1495959 1.1400135 1.1843349 0.9831170 0.6136951
## 2015 0.8900821 0.9254749 0.8615884 1.2668186 1.5839518
## 2016 0.9329225 NA NA NA NA
## 2017
##
## $figure
## [1] 1.1536745 0.9261272 0.7002633 0.7396729 0.8814532 0.6454082 0.7402740
## [8] 1.1617698 1.2774791 1.3474468 1.1888050 1.2376261
##
## $type
## [1] "multiplicative"
##
## attr(,"class")
## [1] "decomposed.ts"We simply check the four components
plot(multi_decomp_PM25)
multi_decomp## $x
## PM2.5 PM10 SO2 NO2 CO O3
## Mar 2013 106.69892 130.19355 41.782387 63.42723 1563.6962 49.67568
## Apr 2013 78.82778 93.94167 22.014413 42.76404 1000.7417 50.78922
## May 2013 81.71640 129.03360 26.635918 52.47490 1094.1250 71.12242
## Jun 2013 105.67153 118.43681 14.815358 52.75863 1628.0139 69.63165
## Jul 2013 68.14651 73.75403 7.801311 45.31321 1223.7702 84.50378
## Aug 2013 59.41532 81.54301 6.996331 45.75652 1075.8065 86.94474
## Sep 2013 61.74306 117.49028 13.512820 57.73660 1326.5194 49.56147
## Oct 2013 98.97849 133.95833 15.550846 73.50200 1392.0699 28.22625
## Nov 2013 84.30972 111.67361 23.508333 58.00556 1575.4167 19.07793
## Dec 2013 92.30914 121.84812 44.816955 66.48069 2213.8441 12.87716
## Jan 2014 113.49194 152.32863 61.379032 79.61559 2171.3710 12.22043
## Feb 2014 156.06399 176.36310 67.059524 74.99405 2458.0357 18.06548
## Mar 2014 98.66667 157.95161 40.067204 66.39785 1489.1129 47.58333
## Apr 2014 86.64444 141.04306 18.758333 54.85417 1075.8333 68.79861
## May 2014 59.18804 112.96250 14.621640 47.10403 934.5430 92.11142
## Jun 2014 58.03889 81.15000 6.341667 46.40833 990.5556 103.63750
## Jul 2014 85.52151 110.45161 5.244624 40.52151 907.9301 104.85215
## Aug 2014 64.41331 91.18616 4.044624 49.18696 1027.1505 94.55497
## Sep 2014 70.99903 97.71708 5.679167 59.13194 1162.5000 53.78361
## Oct 2014 114.25806 143.46505 8.204301 76.72177 1372.3118 26.74059
## Nov 2014 103.31708 142.29014 14.245139 77.05292 1785.4167 22.32083
## Dec 2014 67.94247 111.75591 33.370027 63.90403 1873.9247 29.50847
## Jan 2015 103.28199 128.48925 39.075672 76.75376 2011.6935 24.22755
## Feb 2015 102.95833 133.78869 29.120536 59.45833 1557.1429 38.70536
## Mar 2015 87.32258 155.15323 23.263441 59.77419 1257.3925 54.28763
## Apr 2015 71.85556 121.17083 9.693056 49.62222 835.8333 78.03472
## May 2015 55.34543 93.78898 9.059140 41.90726 779.1667 98.06855
## Jun 2015 59.44583 81.00139 6.877778 37.44861 865.8333 92.75417
## Jul 2015 61.57124 77.40188 4.935484 38.15995 978.3602 95.05780
## Aug 2015 45.68548 67.98118 3.108871 35.40726 909.6774 100.36694
## Sep 2015 53.15000 68.63472 4.965278 43.25139 956.6667 58.35278
## Oct 2015 77.78226 98.78629 5.424731 55.75672 1043.9516 36.92473
## Nov 2015 125.42639 131.26806 14.548611 60.19444 2085.4167 14.15139
## Dec 2015 165.81989 175.36425 24.176075 73.86290 3024.3280 17.96102
## Jan 2016 75.26210 88.44892 24.372312 52.94892 1639.1129 28.16935
## Feb 2016 48.35201 61.49856 17.149425 34.41810 933.9080 47.92385
## Mar 2016 95.18952 130.83737 20.548387 53.99194 1223.9247 48.20565
## Apr 2016 67.05417 109.42500 11.688889 41.57083 852.0833 72.54167
## May 2016 55.25806 95.65995 9.151882 37.45833 724.3280 99.22043
## Jun 2016 64.08889 82.17778 5.462500 34.99444 865.8333 126.60556
## Jul 2016 74.10753 82.06452 3.322581 34.48925 997.9839 96.86290
## Aug 2016 50.55242 64.67608 2.659946 39.72849 932.6613 76.13575
## Sep 2016 59.25139 70.65417 2.827778 50.75833 870.1389 56.39444
## Oct 2016 83.71640 94.86962 3.310484 61.01210 1246.5054 20.25538
## Nov 2016 106.37361 136.37778 10.468056 71.47778 1812.7778 14.05556
## Dec 2016 156.83468 169.18011 17.418011 89.91532 2604.1667 15.15188
## Jan 2017 132.08333 149.47984 18.594086 71.23522 2254.3011 27.93952
## Feb 2017 77.61905 90.79464 18.520833 56.49405 1173.6607 40.98810
## TEMP PRES DEWP RAIN WSPM
## Mar 2013 6.373252688 1011.6395 -6.3188172 0.0236559140 1.753495
## Apr 2013 12.599166667 1007.2869 -2.8651389 0.0141666667 2.223472
## May 2013 21.787903226 1002.1239 8.4520161 0.0076612903 1.771237
## Jun 2013 23.783055556 999.0772 17.5343056 0.1015277778 1.355000
## Jul 2013 27.156451613 995.0235 21.1831989 0.2802419355 1.359946
## Aug 2013 27.257661290 998.2694 20.0935484 0.0907258065 1.416398
## Sep 2013 20.487361111 1008.3138 14.5504167 0.1150000000 1.160972
## Oct 2013 13.199865591 1015.2367 5.3115591 0.0170698925 1.337366
## Nov 2013 5.880555556 1016.0646 -7.1959722 0.0008333333 1.769028
## Dec 2013 -0.005241935 1019.1534 -13.2763441 0.0000000000 1.699866
## Jan 2014 0.173655914 1019.2828 -12.6904570 0.0000000000 1.618548
## Feb 2014 0.089434524 1021.6240 -9.5802083 0.0098214286 1.438244
## Mar 2014 10.513844086 1012.8694 -5.8724462 0.0001344086 1.810215
## Apr 2014 17.184027778 1009.5782 3.9636111 0.0180555556 1.615556
## May 2014 21.865188172 1000.7228 6.9375000 0.0915322581 2.020027
## Jun 2014 24.901944444 999.3411 16.3420833 0.1980555556 1.393472
## Jul 2014 28.287634409 997.8254 19.5525538 0.0581989247 1.479973
## Aug 2014 26.208736559 1001.8782 18.1295699 0.1381720430 1.395833
## Sep 2014 21.123472222 1007.9142 13.8113889 0.0547222222 1.310833
## Oct 2014 14.044892473 1013.6585 6.2706989 0.0182795699 1.217070
## Nov 2014 6.371111111 1021.8025 -5.1972222 0.0004166667 1.538472
## Dec 2014 -0.226478495 1025.9004 -16.1875000 0.0000000000 2.189113
## Jan 2015 -0.125537634 1020.9488 -13.7850806 0.0005376344 1.604704
## Feb 2015 1.743154762 1017.6015 -12.4601190 0.0168154762 1.811905
## Mar 2015 8.439861751 1016.8734 -9.8809140 0.0088709677 2.213575
## Apr 2015 15.630138889 1010.8733 1.6945833 0.0556944444 2.483056
## May 2015 21.455510753 1003.4489 6.6134409 0.0501344086 2.471102
## Jun 2015 24.537777778 1000.3461 14.3013889 0.1362500000 1.980278
## Jul 2015 26.397849462 1001.2784 18.5057796 0.2701612903 1.627285
## Aug 2015 26.435752688 1003.4042 18.4461022 0.1258064516 1.615457
## Sep 2015 20.600833333 1011.3549 13.7698611 0.1372222222 1.601944
## Oct 2015 14.319758065 1015.7254 4.1530914 0.0190860215 1.848790
## Nov 2015 2.847777778 1023.4250 -1.2023611 0.0522222222 1.548056
## Dec 2015 -0.362768817 1024.0706 -7.2271505 0.0028225806 1.856452
## Jan 2016 -4.550000000 1025.9500 -18.0596774 0.0006720430 2.115054
## Feb 2016 1.398419540 1022.5598 -15.0882184 0.0181034483 2.449138
## Mar 2016 9.201881720 1016.7401 -8.7526882 0.0000000000 2.049866
## Apr 2016 16.454722222 1007.8117 -0.3329167 0.0066666667 2.382361
## May 2016 21.672849462 1005.5414 6.2018817 0.0458333333 2.207796
## Jun 2016 25.735833333 1000.7619 14.6834722 0.0991666667 1.803056
## Jul 2016 27.699462366 1000.6353 20.7272849 0.4233870968 1.698925
## Aug 2016 27.863306452 1003.5901 19.2868280 0.0724462366 1.618414
## Sep 2016 22.197344026 1009.3406 14.0559722 0.1598611111 1.554444
## Oct 2016 13.338648073 1017.1267 7.2780914 0.1174731183 1.476882
## Nov 2016 4.414027778 1020.5669 -3.7584722 0.0073611111 1.557778
## Dec 2016 0.640725806 1023.4661 -9.2724462 0.0000000000 1.435618
## Jan 2017 -1.140412186 1025.0380 -12.7756720 0.0004032258 1.969220
## Feb 2017 2.661532738 1022.0206 -13.6276786 0.0061011905 1.953869
##
## $seasonal
## Jan Feb Mar Apr May Jun Jul
## 2013 0.5789615 0.9512677 1.2078615 1.6021536 1.8483973
## 2014 0.2785447 0.3692298 0.5789615 0.9512677 1.2078615 1.6021536 1.8483973
## 2015 0.2785447 0.3692298 0.5789615 0.9512677 1.2078615 1.6021536 1.8483973
## 2016 0.2785447 0.3692298 0.5789615 0.9512677 1.2078615 1.6021536 1.8483973
## 2017 0.2785447 0.3692298 0.5789615 0.9512677 1.2078615 1.6021536 1.8483973
## 2018 0.2785447 0.3692298 0.5789615 0.9512677 1.2078615 1.6021536 1.8483973
## 2019 0.2785447 0.3692298 0.5789615 0.9512677 1.2078615 1.6021536 1.8483973
## 2020 0.2785447 0.3692298 0.5789615 0.9512677 1.2078615 1.6021536 1.8483973
## 2021 0.2785447 0.3692298 0.5789615 0.9512677 1.2078615 1.6021536 1.8483973
## 2022 0.2785447 0.3692298 0.5789615 0.9512677 1.2078615 1.6021536 1.8483973
## 2023 0.2785447 0.3692298 0.5789615 0.9512677 1.2078615 1.6021536 1.8483973
## 2024 0.2785447 0.3692298 0.5789615 0.9512677 1.2078615 1.6021536 1.8483973
## 2025 0.2785447 0.3692298 0.5789615 0.9512677 1.2078615 1.6021536 1.8483973
## 2026 0.2785447 0.3692298 0.5789615 0.9512677 1.2078615 1.6021536 1.8483973
## 2027 0.2785447 0.3692298 0.5789615 0.9512677 1.2078615 1.6021536 1.8483973
## 2028 0.2785447 0.3692298 0.5789615 0.9512677 1.2078615 1.6021536 1.8483973
## 2029 0.2785447 0.3692298 0.5789615 0.9512677 1.2078615 1.6021536 1.8483973
## 2030 0.2785447 0.3692298 0.5789615 0.9512677 1.2078615 1.6021536 1.8483973
## 2031 0.2785447 0.3692298 0.5789615 0.9512677 1.2078615 1.6021536 1.8483973
## 2032 0.2785447 0.3692298 0.5789615 0.9512677 1.2078615 1.6021536 1.8483973
## 2033 0.2785447 0.3692298 0.5789615 0.9512677 1.2078615 1.6021536 1.8483973
## 2034 0.2785447 0.3692298 0.5789615 0.9512677 1.2078615 1.6021536 1.8483973
## 2035 0.2785447 0.3692298 0.5789615 0.9512677 1.2078615 1.6021536 1.8483973
## 2036 0.2785447 0.3692298 0.5789615 0.9512677 1.2078615 1.6021536 1.8483973
## 2037 0.2785447 0.3692298 0.5789615 0.9512677 1.2078615 1.6021536 1.8483973
## 2038 0.2785447 0.3692298 0.5789615 0.9512677 1.2078615 1.6021536 1.8483973
## 2039 0.2785447 0.3692298 0.5789615 0.9512677 1.2078615 1.6021536 1.8483973
## 2040 0.2785447 0.3692298 0.5789615 0.9512677 1.2078615 1.6021536 1.8483973
## 2041 0.2785447 0.3692298 0.5789615 0.9512677 1.2078615 1.6021536 1.8483973
## 2042 0.2785447 0.3692298 0.5789615 0.9512677 1.2078615 1.6021536 1.8483973
## 2043 0.2785447 0.3692298 0.5789615 0.9512677 1.2078615 1.6021536 1.8483973
## 2044 0.2785447 0.3692298 0.5789615 0.9512677 1.2078615 1.6021536 1.8483973
## 2045 0.2785447 0.3692298 0.5789615 0.9512677 1.2078615 1.6021536 1.8483973
## 2046 0.2785447 0.3692298 0.5789615 0.9512677 1.2078615 1.6021536 1.8483973
## 2047 0.2785447 0.3692298 0.5789615 0.9512677 1.2078615 1.6021536 1.8483973
## 2048 0.2785447 0.3692298 0.5789615 0.9512677 1.2078615 1.6021536 1.8483973
## 2049 0.2785447 0.3692298 0.5789615 0.9512677 1.2078615 1.6021536 1.8483973
## 2050 0.2785447 0.3692298 0.5789615 0.9512677 1.2078615 1.6021536 1.8483973
## 2051 0.2785447 0.3692298 0.5789615 0.9512677 1.2078615 1.6021536 1.8483973
## 2052 0.2785447 0.3692298 0.5789615 0.9512677 1.2078615 1.6021536 1.8483973
## 2053 0.2785447 0.3692298 0.5789615 0.9512677 1.2078615 1.6021536 1.8483973
## 2054 0.2785447 0.3692298 0.5789615 0.9512677 1.2078615 1.6021536 1.8483973
## 2055 0.2785447 0.3692298 0.5789615 0.9512677 1.2078615 1.6021536 1.8483973
## 2056 0.2785447 0.3692298 0.5789615 0.9512677 1.2078615 1.6021536 1.8483973
## 2057 0.2785447 0.3692298
## Aug Sep Oct Nov Dec
## 2013 1.6237867 1.4283454 1.0022651 0.6628109 0.4463759
## 2014 1.6237867 1.4283454 1.0022651 0.6628109 0.4463759
## 2015 1.6237867 1.4283454 1.0022651 0.6628109 0.4463759
## 2016 1.6237867 1.4283454 1.0022651 0.6628109 0.4463759
## 2017 1.6237867 1.4283454 1.0022651 0.6628109 0.4463759
## 2018 1.6237867 1.4283454 1.0022651 0.6628109 0.4463759
## 2019 1.6237867 1.4283454 1.0022651 0.6628109 0.4463759
## 2020 1.6237867 1.4283454 1.0022651 0.6628109 0.4463759
## 2021 1.6237867 1.4283454 1.0022651 0.6628109 0.4463759
## 2022 1.6237867 1.4283454 1.0022651 0.6628109 0.4463759
## 2023 1.6237867 1.4283454 1.0022651 0.6628109 0.4463759
## 2024 1.6237867 1.4283454 1.0022651 0.6628109 0.4463759
## 2025 1.6237867 1.4283454 1.0022651 0.6628109 0.4463759
## 2026 1.6237867 1.4283454 1.0022651 0.6628109 0.4463759
## 2027 1.6237867 1.4283454 1.0022651 0.6628109 0.4463759
## 2028 1.6237867 1.4283454 1.0022651 0.6628109 0.4463759
## 2029 1.6237867 1.4283454 1.0022651 0.6628109 0.4463759
## 2030 1.6237867 1.4283454 1.0022651 0.6628109 0.4463759
## 2031 1.6237867 1.4283454 1.0022651 0.6628109 0.4463759
## 2032 1.6237867 1.4283454 1.0022651 0.6628109 0.4463759
## 2033 1.6237867 1.4283454 1.0022651 0.6628109 0.4463759
## 2034 1.6237867 1.4283454 1.0022651 0.6628109 0.4463759
## 2035 1.6237867 1.4283454 1.0022651 0.6628109 0.4463759
## 2036 1.6237867 1.4283454 1.0022651 0.6628109 0.4463759
## 2037 1.6237867 1.4283454 1.0022651 0.6628109 0.4463759
## 2038 1.6237867 1.4283454 1.0022651 0.6628109 0.4463759
## 2039 1.6237867 1.4283454 1.0022651 0.6628109 0.4463759
## 2040 1.6237867 1.4283454 1.0022651 0.6628109 0.4463759
## 2041 1.6237867 1.4283454 1.0022651 0.6628109 0.4463759
## 2042 1.6237867 1.4283454 1.0022651 0.6628109 0.4463759
## 2043 1.6237867 1.4283454 1.0022651 0.6628109 0.4463759
## 2044 1.6237867 1.4283454 1.0022651 0.6628109 0.4463759
## 2045 1.6237867 1.4283454 1.0022651 0.6628109 0.4463759
## 2046 1.6237867 1.4283454 1.0022651 0.6628109 0.4463759
## 2047 1.6237867 1.4283454 1.0022651 0.6628109 0.4463759
## 2048 1.6237867 1.4283454 1.0022651 0.6628109 0.4463759
## 2049 1.6237867 1.4283454 1.0022651 0.6628109 0.4463759
## 2050 1.6237867 1.4283454 1.0022651 0.6628109 0.4463759
## 2051 1.6237867 1.4283454 1.0022651 0.6628109 0.4463759
## 2052 1.6237867 1.4283454 1.0022651 0.6628109 0.4463759
## 2053 1.6237867 1.4283454 1.0022651 0.6628109 0.4463759
## 2054 1.6237867 1.4283454 1.0022651 0.6628109 0.4463759
## 2055 1.6237867 1.4283454 1.0022651 0.6628109 0.4463759
## 2056 1.6237867 1.4283454 1.0022651 0.6628109 0.4463759
## 2057
##
## $trend
## [,1] [,2] [,3] [,4] [,5] [,6] [,7]
## Mar 2013 NA NA NA NA NA NA NA
## Apr 2013 NA NA NA NA NA NA NA
## May 2013 NA NA NA NA NA NA NA
## Jun 2013 NA NA NA NA NA NA NA
## Jul 2013 NA NA NA NA NA NA NA
## Aug 2013 NA NA NA NA NA NA NA
## Sep 2013 91.94639 121.20365 28.75130 59.52619 1557.177 45.97084 13.40445
## Oct 2013 91.93741 124.32279 28.54417 60.15372 1557.198 46.63405 13.76801
## Nov 2013 91.32442 125.61572 27.90790 60.43369 1553.677 48.25898 13.96227
## Dec 2013 88.40104 123.39247 27.05424 59.94531 1520.467 50.55043 14.01211
## Jan 2014 87.14031 123.36792 26.59464 59.48106 1480.747 52.81519 14.10586
## Feb 2014 88.07252 125.29879 26.36512 59.42434 1465.559 53.98013 14.10929
## Mar 2014 88.66643 124.87670 25.91573 59.62542 1456.698 54.47315 14.09209
## Apr 2014 89.68875 124.44893 25.28322 59.81771 1449.040 54.58717 14.15380
## May 2014 91.11737 126.12073 24.59115 60.74551 1456.967 54.66039 14.20945
## Jun 2014 90.89406 126.97591 23.72823 61.43179 1451.554 55.48848 14.22067
## Jul 2014 89.45337 125.56210 22.32197 61.20519 1430.737 56.68175 14.19899
## Aug 2014 86.81522 122.79486 19.81187 60.43862 1386.547 58.04204 14.25543
## Sep 2014 84.12981 120.90432 17.53092 59.51532 1339.355 59.18138 14.23792
## Oct 2014 83.04094 119.95971 16.45304 59.02133 1319.700 59.84556 14.08676
## Nov 2014 82.26463 118.33281 15.84355 58.58680 1303.226 60.47862 14.00494
## Dec 2014 82.16314 117.52772 15.63412 57.99695 1291.555 60.27336 13.97270
## Jan 2015 81.22384 116.14445 15.64358 57.52523 1289.293 59.41179 13.87878
## Feb 2015 79.44558 113.80051 15.59171 56.85268 1287.332 59.24585 13.80950
## Mar 2015 77.92155 111.62187 15.52297 55.61683 1273.861 59.67840 13.79718
## Apr 2015 75.65801 108.54849 15.37741 54.08160 1251.603 60.29312 13.78686
## May 2015 75.05941 106.22762 15.27424 52.50562 1250.422 60.37707 13.65151
## Jun 2015 80.05886 108.41871 14.90380 52.21813 1310.855 59.55553 13.49902
## Jul 2015 82.96959 109.40072 13.90808 51.64122 1343.264 59.23863 13.30899
## Aug 2015 79.52683 104.72028 12.79665 49.60601 1301.772 59.78697 13.11027
## Sep 2015 77.57935 100.69503 12.18472 48.32174 1274.409 59.91766 13.12766
## Oct 2015 77.70708 99.19246 12.15476 47.74534 1273.692 59.43537 13.19377
## Nov 2015 77.50339 98.78101 12.24178 47.22449 1272.084 59.25449 13.23718
## Dec 2015 77.69321 98.90798 12.18667 46.93686 1269.799 60.71295 13.29616
## Jan 2016 78.40901 99.15127 12.06050 46.68166 1270.617 62.19864 13.40031
## Feb 2016 79.13415 99.20784 11.97459 46.70876 1272.392 61.26422 13.51402
## Mar 2016 79.59116 99.15427 11.86682 47.20160 1269.745 60.17299 13.64003
## Apr 2016 80.09264 99.07522 11.68967 47.73337 1274.579 59.39684 13.66567
## May 2016 79.54603 99.12493 11.43155 48.42248 1271.659 58.69829 13.69005
## Jun 2016 78.37778 99.08016 10.97994 49.56147 1242.792 58.57725 13.79712
## Jul 2016 80.37095 101.36544 10.45759 50.99225 1250.918 58.45062 13.98100
## Aug 2016 83.95796 105.12907 10.27398 52.67401 1286.541 58.15206 14.17570
## Sep 2016 NA NA NA NA NA NA NA
## Oct 2016 NA NA NA NA NA NA NA
## Nov 2016 NA NA NA NA NA NA NA
## Dec 2016 NA NA NA NA NA NA NA
## Jan 2017 NA NA NA NA NA NA NA
## Feb 2017 NA NA NA NA NA NA NA
## [,8] [,9] [,10] [,11]
## Mar 2013 NA NA NA NA
## Apr 2013 NA NA NA NA
## May 2013 NA NA NA NA
## Jun 2013 NA NA NA NA
## Jul 2013 NA NA NA NA
## Aug 2013 NA NA NA NA
## Sep 2013 1009.476 2.951774 0.05407861 1.577661
## Oct 2013 1009.623 3.254904 0.05326058 1.554694
## Nov 2013 1009.660 3.476331 0.05691724 1.539731
## Dec 2013 1009.612 3.363550 0.06443386 1.551700
## Jan 2014 1009.740 3.245931 0.05920406 1.558304
## Feb 2014 1010.007 3.096155 0.05192919 1.562449
## Mar 2014 1010.141 2.983529 0.05139454 1.567836
## Apr 2014 1010.058 2.992701 0.04893337 1.569068
## May 2014 1010.232 3.115946 0.04896641 1.554449
## Jun 2014 1010.752 3.077929 0.04894905 1.565228
## Jul 2014 1011.103 2.911022 0.04897145 1.585036
## Aug 2014 1011.004 2.745416 0.04928527 1.600029
## Sep 2014 1011.004 2.458400 0.04994072 1.632404
## Oct 2014 1011.224 2.196838 0.05187303 1.685357
## Nov 2014 1011.392 2.088793 0.05171640 1.740298
## Dec 2014 1011.547 1.990261 0.04741626 1.783543
## Jan 2015 1011.733 1.861617 0.05367280 1.814131
## Feb 2015 1011.941 1.831190 0.06198933 1.829420
## Mar 2015 1012.148 1.842649 0.06491159 1.850700
## Apr 2015 1012.377 1.752685 0.06838270 1.889152
## May 2015 1012.531 1.830903 0.07057486 1.915873
## Jun 2015 1012.522 2.370704 0.07285104 1.902411
## Jul 2015 1012.654 2.565944 0.07297424 1.909815
## Aug 2015 1013.069 2.278331 0.07303351 1.957631
## Sep 2015 1013.270 2.215837 0.07271755 1.977361
## Oct 2015 1013.137 2.178367 0.07030510 1.966344
## Nov 2015 1013.097 2.076739 0.06808307 1.951177
## Dec 2015 1013.201 2.075511 0.06635872 1.932822
## Jan 2016 1013.192 2.183994 0.07119799 1.928423
## Feb 2016 1013.173 2.311587 0.07535905 1.931531
## Mar 2016 1013.097 2.358539 0.07407900 1.929675
## Apr 2016 1013.071 2.500668 0.07912175 1.912200
## May 2016 1013.010 2.524372 0.08135200 1.897109
## Jun 2016 1012.866 2.332647 0.07936518 1.879979
## Jul 2016 1012.803 2.467593 0.07923637 1.856368
## Aug 2016 1012.742 2.748616 0.07872507 1.829655
## Sep 2016 NA NA NA NA
## Oct 2016 NA NA NA NA
## Nov 2016 NA NA NA NA
## Dec 2016 NA NA NA NA
## Jan 2017 NA NA NA NA
## Feb 2017 NA NA NA NA
##
## $random
## x/seasonal.x.PM2.5 x/seasonal.x.PM10 x/seasonal.x.SO2 x/seasonal.x.NO2
## Mar 2013 NA NA NA NA
## Apr 2013 NA NA NA NA
## May 2013 NA NA NA NA
## Jun 2013 NA NA NA NA
## Jul 2013 NA NA NA NA
## Aug 2013 NA NA NA NA
## Sep 2013 0.4701324 0.6786612 0.3290449 0.6790627
## Oct 2013 1.0741526 1.0750691 0.5435682 1.2191412
## Nov 2013 1.3928397 1.3412723 1.2708814 1.4481077
## Dec 2013 2.3393035 2.2122256 3.7111312 2.4845030
## Jan 2014 4.6757474 4.4328640 8.2857359 4.8053447
## Feb 2014 4.7991632 3.8120982 6.8886468 3.4179495
## Mar 2014 1.9220363 2.1847060 2.6703976 1.9234147
## Apr 2014 1.0155470 1.1914006 0.7799362 0.9640001
## May 2014 0.5377936 0.7415333 0.4922663 0.6419878
## Jun 2014 0.3985469 0.3988991 0.1668145 0.4715184
## Jul 2014 0.5172295 0.4759027 0.1271120 0.3581806
## Aug 2014 0.4569311 0.4573195 0.1257256 0.5011947
## Sep 2014 0.5908391 0.5658423 0.2268019 0.6956010
## Oct 2014 1.3728149 1.1932408 0.4975225 1.2969613
## Nov 2014 1.8948262 1.8141785 1.3565146 1.9842650
## Dec 2014 1.8525228 2.1302445 4.7817002 2.4684388
## Jan 2015 4.5650571 3.9716725 8.9675850 4.7901207
## Feb 2015 3.5099018 3.1840393 5.0583505 2.8324682
## Mar 2015 1.9356166 2.4008325 2.5885075 1.8563413
## Apr 2015 0.9983957 1.1734689 0.6626356 0.9645483
## May 2015 0.6104632 0.7309661 0.4910325 0.6607944
## Jun 2015 0.4634553 0.4663200 0.2880361 0.4476207
## Jul 2015 0.4014797 0.3827684 0.1919849 0.3997753
## Aug 2015 0.3537819 0.3997872 0.1496158 0.4395710
## Sep 2015 0.4796494 0.4772024 0.2852953 0.6266489
## Oct 2015 0.9987052 0.9936545 0.4452966 1.1651549
## Nov 2015 2.4416231 2.0049151 1.7930293 1.9230897
## Dec 2015 4.7813753 3.9719975 4.4442642 3.5254259
## Jan 2016 3.4460015 3.2025756 7.2549857 4.0720772
## Feb 2016 1.6548318 1.6788899 3.8787532 1.9956841
## Mar 2016 2.0657351 2.2791386 2.9908433 1.9757068
## Apr 2016 0.8800968 1.1610443 1.0511590 0.9155118
## May 2016 0.5751221 0.7989694 0.6628087 0.6404486
## Jun 2016 0.5103706 0.5176826 0.3105184 0.4407078
## Jul 2016 0.4988476 0.4379960 0.1718891 0.3659184
## Aug 2016 0.3708097 0.3788714 0.1594429 0.4644904
## Sep 2016 NA NA NA NA
## Oct 2016 NA NA NA NA
## Nov 2016 NA NA NA NA
## Dec 2016 NA NA NA NA
## Jan 2017 NA NA NA NA
## Feb 2017 NA NA NA NA
## x/seasonal.x.CO x/seasonal.x.O3 x/seasonal.x.TEMP x/seasonal.x.PRES
## Mar 2013 NA NA NA NA
## Apr 2013 NA NA NA NA
## May 2013 NA NA NA NA
## Jun 2013 NA NA NA NA
## Jul 2013 NA NA NA NA
## Aug 2013 NA NA NA NA
## Sep 2013 0.5964067 0.7547941 1.0700491783 0.6993048
## Oct 2013 0.8919380 0.6039034 0.9565675996 1.0032880
## Nov 2013 1.5298365 0.5964356 0.6354374035 1.5182968
## Dec 2013 3.2618892 0.5706826 -0.0008380838 2.2614352
## Jan 2014 5.2645158 0.8306781 0.0441972336 3.6240171
## Feb 2014 4.5424280 0.9063975 0.0171673513 2.7394908
## Mar 2014 1.7656659 1.5087689 1.2886545842 1.7318961
## Apr 2014 0.7804800 1.3249100 1.2762892222 1.0507290
## May 2014 0.5310464 1.3951589 1.2739687396 0.8201167
## Jun 2014 0.4259333 1.1657621 1.0929717397 0.6171134
## Jul 2014 0.3433185 1.0007804 1.0778141675 0.5339051
## Aug 2014 0.4562161 1.0032582 1.1322357224 0.6102853
## Sep 2014 0.6076649 0.6362556 1.0386892246 0.6979714
## Oct 2014 1.0375168 0.4458168 0.9947749536 1.0001416
## Nov 2014 2.0669520 0.5568253 0.6863479112 1.5242558
## Dec 2014 3.2504131 1.0967825 -0.0363116507 2.2720517
## Jan 2015 5.6016435 1.4640034 -0.0324733968 3.6227896
## Feb 2015 3.2759779 1.7693606 0.3418701821 2.7234910
## Mar 2015 1.7049005 1.5712095 1.0565627263 1.7352954
## Apr 2015 0.7020212 1.3605590 1.1917764352 1.0496674
## May 2015 0.5158896 1.3447471 1.3011914054 0.8204836
## Jun 2015 0.4122640 0.9720916 1.1345634475 0.6166541
## Jul 2015 0.3940415 0.8681353 1.0730701936 0.5349317
## Aug 2015 0.4303517 1.0338442 1.2417979821 0.6099690
## Sep 2015 0.5255553 0.6818258 1.0986623118 0.6987873
## Oct 2015 0.8177741 0.6198545 1.0828896712 1.0002889
## Nov 2015 2.4733603 0.3603199 0.3245793951 1.5241071
## Dec 2015 5.3357205 0.6627487 -0.0611227761 2.2642971
## Jan 2016 4.6312622 1.6259273 -1.2189943480 3.6352950
## Feb 2016 1.9878625 2.1185953 0.2802566940 2.7334329
## Mar 2016 1.6649021 1.3837150 1.1652302497 1.7334425
## Apr 2016 0.7027690 1.2838712 1.2657761794 1.0457714
## May 2016 0.4715715 1.3994537 1.3106714925 0.8218053
## Jun 2016 0.4348422 1.3490239 1.1642481136 0.6167009
## Jul 2016 0.4316177 0.8965469 1.0718592053 0.5345097
## Aug 2016 0.4464486 0.8062961 1.2104845181 0.6102789
## Sep 2016 NA NA NA NA
## Oct 2016 NA NA NA NA
## Nov 2016 NA NA NA NA
## Dec 2016 NA NA NA NA
## Jan 2017 NA NA NA NA
## Feb 2017 NA NA NA NA
## x/seasonal.x.DEWP x/seasonal.x.RAIN x/seasonal.x.WSPM
## Mar 2013 NA NA NA
## Apr 2013 NA NA NA
## May 2013 NA NA NA
## Jun 2013 NA NA NA
## Jul 2013 NA NA NA
## Aug 2013 NA NA NA
## Sep 2013 3.4511118 1.488809394 0.5151989
## Oct 2013 1.6281753 0.319773353 0.8582672
## Nov 2013 -3.1230488 0.022089470 1.7334058
## Dec 2013 -8.8425974 0.000000000 2.4541779
## Jan 2014 -14.0359936 0.000000000 3.7288813
## Feb 2014 -8.3802223 0.512231566 2.4930449
## Mar 2014 -3.3996882 0.004517107 1.9942515
## Apr 2014 1.3922750 0.387884998 1.0823743
## May 2014 1.8432996 1.547600117 1.0758793
## Jun 2014 3.3139400 2.525448835 0.5556696
## Jul 2014 3.6338142 0.642949165 0.5051488
## Aug 2014 4.0667768 1.726529543 0.5372505
## Sep 2014 3.9332496 0.767141930 0.5621943
## Oct 2014 2.8479693 0.351594261 0.7205116
## Nov 2014 -3.7539314 0.012155444 1.3337564
## Dec 2014 -18.2208623 0.000000000 2.7496911
## Jan 2015 -26.5842339 0.035961514 3.1756419
## Feb 2015 -18.4285853 0.734675356 2.6824103
## Mar 2015 -9.2620038 0.236047321 2.0658963
## Apr 2015 1.0163807 0.856175750 1.3817098
## May 2015 2.9905075 0.588123761 1.0678418
## Jun 2015 3.7652753 1.167337983 0.6497070
## Jul 2015 3.9017995 2.002895060 0.4609746
## Aug 2015 4.9860743 1.060844563 0.5082011
## Sep 2015 4.3506946 1.321149496 0.5671896
## Oct 2015 1.9022074 0.270860670 0.9380922
## Nov 2015 -0.8735008 1.157248481 1.1970166
## Dec 2015 -7.8008382 0.095290065 2.1517460
## Jan 2016 -29.6868191 0.033887106 3.9375337
## Feb 2016 -17.6779109 0.650622523 3.4341147
## Mar 2016 -6.4098642 0.000000000 1.8348120
## Apr 2016 -0.1399512 0.088574791 1.3096994
## May 2016 2.0340097 0.466440336 0.9634952
## Jun 2016 3.9289423 0.779886790 0.5986210
## Jul 2016 4.5443690 2.890797901 0.4951249
## Aug 2016 4.3213338 0.566726820 0.5447426
## Sep 2016 NA NA NA
## Oct 2016 NA NA NA
## Nov 2016 NA NA NA
## Dec 2016 NA NA NA
## Jan 2017 NA NA NA
## Feb 2017 NA NA NA
##
## $figure
## [1] 0.5789615 0.9512677 1.2078615 1.6021536 1.8483973 1.6237867 1.4283454
## [8] 1.0022651 0.6628109 0.4463759 0.2785447 0.3692298
##
## $type
## [1] "multiplicative"
##
## attr(,"class")
## [1] "decomposed.ts"Now, we check the fundamental changes of different air pollutants and weather conditions in 2014 to 2017.
plot(multi_decomp$x[,1:6])
plot(multi_decomp$x[,7:11])
Then we also check the fundamental changes in the four components in different column in 2014 to 2017.
In the trend, we found that the trend of air pollutants(PM2.5, PM10, SO2, NO2, CO) shows a remarkable decline since 2014. And the trend of air pollutants(O3) shows a remarkable ascend since 2014.
plot(multi_decomp$seasonal[1:60], type = "l")
plot(multi_decomp$trend[,1:6])
plot(multi_decomp$trend[,7:11])
plot(multi_decomp$random[,1:6])
plot(multi_decomp$random[,7:11])
We found that the multiplicative decomposition model and additive decomposition model shows similar result.
Moving average smoothing (monthly)
Building Seasonal-Trend decomposition model (STL)
STL.PM2.5<- stl( ts_by_month[,'PM2.5'] , t.window = 13, s.window = 'periodic')
plot(STL.PM2.5)
STL.PM10<- stl( ts_by_month[,'PM10'] , t.window = 13, s.window = 'periodic')
plot(STL.PM10)
STL.NO2<- stl( ts_by_month[,'NO2'] , t.window = 13, s.window = 'periodic')
plot(STL.NO2)
STL.SO2<- stl( ts_by_month[,'NO2'] , t.window = 13, s.window = 'periodic')
plot(STL.SO2)
STL.CO<- stl( ts_by_month[,'CO'] , t.window = 13, s.window = 'periodic')
plot(STL.CO)
STL.O3<- stl( ts_by_month[,'O3'] , t.window = 13, s.window = 'periodic')
plot(STL.O3)
STL.TEMP<- stl( ts_by_month[,'TEMP'] , t.window = 13, s.window = 'periodic')
plot(STL.TEMP)
STL.PRES<- stl( ts_by_month[,'PRES'] , t.window = 13, s.window = 'periodic')
plot(STL.PRES)
STL.RAIN<- stl( ts_by_month[,'RAIN'] , t.window = 13, s.window = 'periodic')
plot(STL.RAIN)
Tesk for random / remainder for the STL model using Ljung-Box Test (monthly)
auto.arima(remainder(STL.PM2.5),trace = T)##
## ARIMA(2,0,2)(1,0,1)[12] with non-zero mean : Inf
## ARIMA(0,0,0) with non-zero mean : 422.7225
## ARIMA(1,0,0)(1,0,0)[12] with non-zero mean : 427.1379
## ARIMA(0,0,1)(0,0,1)[12] with non-zero mean : Inf
## ARIMA(0,0,0) with zero mean : 420.5498
## ARIMA(0,0,0)(1,0,0)[12] with non-zero mean : 424.9196
## ARIMA(0,0,0)(0,0,1)[12] with non-zero mean : 424.5797
## ARIMA(0,0,0)(1,0,1)[12] with non-zero mean : Inf
## ARIMA(1,0,0) with non-zero mean : 424.8169
## ARIMA(0,0,1) with non-zero mean : 423.1371
## ARIMA(1,0,1) with non-zero mean : 422.5173
##
## Best model: ARIMA(0,0,0) with zero mean## Series: remainder(STL.PM2.5)
## ARIMA(0,0,0) with zero mean
##
## sigma^2 = 357.8: log likelihood = -209.23
## AIC=420.46 AICc=420.55 BIC=422.33x <- lapply(1:10, function(i){
p <- Box.test(remainder(STL.PM2.5), lag = i, type = "Ljung-Box")
output <- data.frame(lag = i, p_value = p$p.value)
return(output) }) %>% bind_rows
plot(x = x$lag,
y = x$p_value, ylim = c(0,1),
main = "Series white_noise (PM2.5) - Ljung-Box Test",
xlab = "Lag", ylab = "P-Value")
abline(h = 0.05, col="red", lwd=3, lty=2)
auto.arima(remainder(STL.PM10))## Series: remainder(STL.PM10)
## ARIMA(2,0,1) with zero mean
##
## Coefficients:
## ar1 ar2 ma1
## 0.5851 -0.6317 -0.8254
## s.e. 0.1170 0.1137 0.0924
##
## sigma^2 = 180: log likelihood = -192.29
## AIC=392.57 AICc=393.5 BIC=400.06x <- lapply(1:10, function(i){
p <- Box.test(remainder(STL.PM10), lag = i, type = "Ljung-Box")
output <- data.frame(lag = i, p_value = p$p.value)
return(output) }) %>% bind_rows
plot(x = x$lag,
y = x$p_value, ylim = c(0,1),
main = "Series white_noise(PM10) - Ljung-Box Test",
xlab = "Lag", ylab = "P-Value")
abline(h = 0.05, col="red", lwd=3, lty=2)
auto.arima(remainder(STL.SO2))## Series: remainder(STL.SO2)
## ARIMA(0,0,0) with zero mean
##
## sigma^2 = 32.73: log likelihood = -151.83
## AIC=305.65 AICc=305.74 BIC=307.52x <- lapply(1:10, function(i){
p <- Box.test(remainder(STL.SO2), lag = i, type = "Ljung-Box")
output <- data.frame(lag = i, p_value = p$p.value)
return(output) }) %>% bind_rows
plot(x = x$lag,
y = x$p_value, ylim = c(0,1),
main = "Series white_noise(SO2) - Ljung-Box Test",
xlab = "Lag", ylab = "P-Value")
abline(h = 0.05, col="red", lwd=3, lty=2)
auto.arima(remainder(STL.NO2))## Series: remainder(STL.NO2)
## ARIMA(0,0,0) with zero mean
##
## sigma^2 = 32.73: log likelihood = -151.83
## AIC=305.65 AICc=305.74 BIC=307.52x <- lapply(1:10, function(i){
p <- Box.test(remainder(STL.NO2), lag = i, type = "Ljung-Box")
output <- data.frame(lag = i, p_value = p$p.value)
return(output) }) %>% bind_rows
plot(x = x$lag,
y = x$p_value, ylim = c(0,1),
main = "Series white_noise(NO2) - Ljung-Box Test",
xlab = "Lag", ylab = "P-Value")
abline(h = 0.05, col="red", lwd=3, lty=2)
auto.arima(remainder(STL.CO))## Series: remainder(STL.CO)
## ARIMA(0,0,0) with zero mean
##
## sigma^2 = 53698: log likelihood = -329.5
## AIC=660.99 AICc=661.08 BIC=662.86x <- lapply(1:10, function(i){
p <- Box.test(remainder(STL.CO), lag = i, type = "Ljung-Box")
output <- data.frame(lag = i, p_value = p$p.value)
return(output) }) %>% bind_rows
plot(x = x$lag,
y = x$p_value, ylim = c(0,1),
main = "Series white_noise(CO) - Ljung-Box Test",
xlab = "Lag", ylab = "P-Value")
abline(h = 0.05, col="red", lwd=3, lty=2)
auto.arima(remainder(STL.O3))## Series: remainder(STL.O3)
## ARIMA(0,0,0) with zero mean
##
## sigma^2 = 51.6: log likelihood = -162.76
## AIC=327.51 AICc=327.6 BIC=329.38x <- lapply(1:10, function(i){
p <- Box.test(remainder(STL.O3), lag = i, type = "Ljung-Box")
output <- data.frame(lag = i, p_value = p$p.value)
return(output) }) %>% bind_rows
plot(x = x$lag,
y = x$p_value, ylim = c(0,1),
main = "Series white_noise(O3) - Ljung-Box Test",
xlab = "Lag", ylab = "P-Value")
abline(h = 0.05, col="red", lwd=3, lty=2)
auto.arima(remainder(STL.TEMP))## Series: remainder(STL.TEMP)
## ARIMA(1,0,1) with zero mean
##
## Coefficients:
## ar1 ma1
## 0.3815 -0.8530
## s.e. 0.2102 0.1376
##
## sigma^2 = 0.5325: log likelihood = -52.3
## AIC=110.6 AICc=111.14 BIC=116.21x <- lapply(1:10, function(i){
p <- Box.test(remainder(STL.TEMP), lag = i, type = "Ljung-Box")
output <- data.frame(lag = i, p_value = p$p.value)
return(output) }) %>% bind_rows
plot(x = x$lag,
y = x$p_value, ylim = c(0,1),
main = "Series white_noise(TEMP) - Ljung-Box Test",
xlab = "Lag", ylab = "P-Value")
abline(h = 0.05, col="red", lwd=3, lty=2)
auto.arima(remainder(STL.PRES))## Series: remainder(STL.PRES)
## ARIMA(0,0,0) with zero mean
##
## sigma^2 = 1.942: log likelihood = -84.04
## AIC=170.09 AICc=170.17 BIC=171.96x <- lapply(1:10, function(i){
p <- Box.test(remainder(STL.PRES), lag = i, type = "Ljung-Box")
output <- data.frame(lag = i, p_value = p$p.value)
return(output) }) %>% bind_rows
plot(x = x$lag,
y = x$p_value, ylim = c(0,1),
main = "Series white_noise(PRES) - Ljung-Box Test",
xlab = "Lag", ylab = "P-Value")
abline(h = 0.05, col="red", lwd=3, lty=2)
auto.arima(remainder(STL.RAIN))## Series: remainder(STL.RAIN)
## ARIMA(2,0,0) with zero mean
##
## Coefficients:
## ar1 ar2
## -0.5866 -0.2711
## s.e. 0.1379 0.1360
##
## sigma^2 = 0.001314: log likelihood = 91.96
## AIC=-177.91 AICc=-177.37 BIC=-172.3x <- lapply(1:10, function(i){
p <- Box.test(remainder(STL.RAIN), lag = i, type = "Ljung-Box")
output <- data.frame(lag = i, p_value = p$p.value)
return(output) }) %>% bind_rows
plot(x = x$lag,
y = x$p_value, ylim = c(0,1),
main = "Series white_noise(RAIN) - Ljung-Box Test",
xlab = "Lag", ylab = "P-Value")
abline(h = 0.05, col="red", lwd=3, lty=2)
The Ljung Box test test the white noise of the timeseries data.
For most of the variable, the residual of the model of lag 1 (AR1) is white noise, such as PM2.5, PM10, SO2, NO2, CO, O3) and for the other model (> lag 2) there exhibit serial correlation among the residual.
forcesting for diffrent varible by using ARIMA forecast
forecast(STL.PM2.5, h=5, method = 'arima')## Point Forecast Lo 80 Hi 80 Lo 95 Hi 95
## Mar 2017 86.21735 61.83649 110.59822 48.93003 123.5047
## Apr 2017 79.49162 54.22798 104.75526 40.85421 118.1290
## May 2017 62.30253 36.08973 88.51534 22.21351 102.3916
## Jun 2017 71.63256 45.41976 97.84536 31.54354 111.7216
## Jul 2017 72.55371 46.34091 98.76652 32.46469 112.6427STL.PM2.5 %>% forecast(method="arima", h=15) %>%
autoplot(ylab = 'PM2.5') + ggtitle('Forecasting')
forecast(STL.PM10, h=5, method = 'arima')## Point Forecast Lo 80 Hi 80 Lo 95 Hi 95
## Mar 2017 120.79043 88.517342 153.0635 71.433001 170.1479
## Apr 2017 93.15092 47.509874 138.7920 23.348967 162.9529
## May 2017 84.11630 28.217664 140.0149 -1.373283 169.6059
## Jun 2017 67.14942 2.603237 131.6956 -31.565446 165.8643
## Jul 2017 62.57884 -9.585981 134.7437 -47.787730 172.9454STL.PM10 %>% forecast(method="arima", h=5) %>%
autoplot(ylab = 'PM10') + ggtitle('Forecasting')
forecast(STL.SO2, h=5, method = 'arima')## Point Forecast Lo 80 Hi 80 Lo 95 Hi 95
## Mar 2017 68.14126 59.43630 76.84623 54.82818 81.45435
## Apr 2017 53.15557 43.52385 62.78730 38.42512 67.88602
## May 2017 51.10024 41.46850 60.73198 36.36977 65.83072
## Jun 2017 49.34610 39.07363 59.61857 33.63571 65.05648
## Jul 2017 46.14406 35.26854 57.01957 29.51139 62.77672STL.SO2 %>% forecast(method="arima", h=5) %>%
autoplot(ylab = 'SO2') + ggtitle('Forecasting')
forecast(STL.NO2, h=5, method = 'arima')## Point Forecast Lo 80 Hi 80 Lo 95 Hi 95
## Mar 2017 68.14126 59.43630 76.84623 54.82818 81.45435
## Apr 2017 53.15557 43.52385 62.78730 38.42512 67.88602
## May 2017 51.10024 41.46850 60.73198 36.36977 65.83072
## Jun 2017 49.34610 39.07363 59.61857 33.63571 65.05648
## Jul 2017 46.14406 35.26854 57.01957 29.51139 62.77672# use other mothed
STL.NO2 %>% forecast(method="arima", h=5) %>%
autoplot(ylab = 'NO2') + ggtitle('Forecasting')
forecast(STL.CO, h=5, method = 'arima')## Point Forecast Lo 80 Hi 80 Lo 95 Hi 95
## Mar 2017 973.1480 572.96253 1373.333 361.1172 1585.179
## Apr 2017 541.0066 -24.94106 1106.954 -324.5356 1406.549
## May 2017 493.1916 -199.94991 1186.333 -566.8768 1553.260
## Jun 2017 705.9207 -94.45017 1506.292 -518.1409 1929.982
## Jul 2017 653.5837 -241.25813 1548.425 -714.9588 2022.126STL.CO %>% forecast(method="arima", h=5) %>%
autoplot(ylab = 'CO') + ggtitle('Forecasting')
forecast(STL.O3, h=5, method = 'arima')## Point Forecast Lo 80 Hi 80 Lo 95 Hi 95
## Mar 2017 54.48040 43.83217 65.12862 38.19534 70.76545
## Apr 2017 70.76883 58.73549 82.80218 52.36542 89.17224
## May 2017 92.69411 80.44298 104.94525 73.95762 111.43061
## Jun 2017 100.41208 87.94696 112.87721 81.34833 119.47584
## Jul 2017 97.26549 84.59000 109.94099 77.88000 116.65099STL.O3 %>% forecast(method="arima", h=5) %>%
autoplot(ylab = 'O3') + ggtitle('Forecasting')
forecast(STL.TEMP, h=5, method = 'arima')## Point Forecast Lo 80 Hi 80 Lo 95 Hi 95
## Mar 2017 8.959632 7.553627 10.36564 6.809334 11.10993
## Apr 2017 15.694990 14.288986 17.10099 13.544692 17.84529
## May 2017 21.823893 20.417889 23.22990 19.673595 23.97419
## Jun 2017 24.808395 23.402391 26.21440 22.658097 26.95869
## Jul 2017 27.394304 25.988299 28.80031 25.244006 29.54460STL.TEMP %>% forecast(method="arima", h=5) %>%
autoplot(ylab = 'TEMP') + ggtitle('Forecasting')
forecast(STL.PRES, h=5, method = 'arima')## Point Forecast Lo 80 Hi 80 Lo 95 Hi 95
## Mar 2017 1017.000 1014.9299 1019.070 1013.8341 1020.166
## Apr 2017 1011.356 1009.2789 1013.433 1008.1794 1014.532
## May 2017 1005.427 1003.3427 1007.511 1002.2394 1008.614
## Jun 2017 1002.406 1000.3147 1004.497 999.2077 1005.604
## Jul 2017 1001.271 999.1734 1003.370 998.0628 1004.480STL.PRES %>% forecast(method="arima", h=5) %>%
autoplot(ylab = 'PRES') + ggtitle('Forecasting')
forecast(STL.RAIN, h=5, method = 'arima')## Point Forecast Lo 80 Hi 80 Lo 95 Hi 95
## Mar 2017 0.009683263 -0.04728248 0.06664901 -0.07743833 0.09680485
## Apr 2017 0.022910496 -0.03598979 0.08181078 -0.06716972 0.11299071
## May 2017 0.048501231 -0.01053034 0.10753280 -0.04177976 0.13878222
## Jun 2017 0.133140859 0.07410023 0.19218148 0.04284601 0.22343570
## Jul 2017 0.257254452 0.19821320 0.31629570 0.16695865 0.34755025STL.RAIN %>% forecast(method="arima", h=5) %>%
autoplot(ylab = 'RAIN') + ggtitle('Forecasting')
The forecast plot shows the predict value of diffreient variable of the next five months on difference variable.
Conclusion
We find out that,
The air pollution in Beijing condition are correlated with the weather condition.
The air pollution condition will change in different season.
For all air pollutant except O3, there will be a higher concentration in winter and lower concentration in summer.
For O3, there will be a higher concentration in winter and lower concentration in summer. Air pollution have pattern among hourly,weekly and monthly.